# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/{displaymath}nabla^2u=v,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="\begin{displaymath}
\nabla^2 u = v,
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig45.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img1892.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig45.eps}}
\end{figure}">|; 

$key = q/A'=A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2799.png"
 ALT="$A'= A$">|; 

$key = q/d({A^{icdotsj}}_{kcdotsl})slashds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2850.png"
 ALT="$d({A^{i\cdots j}}_{k\cdots l})/ds$">|; 

$key = q/{displaymath}v=frac{omega}{k}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="\begin{displaymath}
v = \frac{\omega}{k}.
\end{displaymath}">|; 

$key = q/10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="$10^{-1}$">|; 

$key = q/1slashr^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1854.png"
 ALT="$1/r^3$">|; 

$key = q/{{bf{a}times{{bf{b}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="${\bf a}\times{\bf b} = {\bf0}$">|; 

$key = q/A^j=C^{ij}B_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2819.png"
 ALT="$A^j = C^{ij} B_i$">|; 

$key = q/displaystyleA_x({{bf{r})=frac{mu_0}{4pi}intfrac{j_x({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$\displaystyle A_x({\bf r}) = \frac{\mu_0}{4\pi} \int \frac{j_x({\bf r}')}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r}',$">|; 

$key = q/displaystylemu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="$\displaystyle \mu_0$">|; 

$key = q/displaystylelangleUrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2149.png"
 ALT="$\displaystyle \langle U\rangle$">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int \frac{\rho({\bf r}')}
{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r}',$">|; 

$key = q/{displaymath}frac{dF}{dz}=2,z{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1549.png"
 ALT="\begin{displaymath}
\frac{dF}{dz} = 2  z
\end{displaymath}">|; 

$key = q/nablaphi=-{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="$\nabla\phi = - {\bf E}$">|; 

$key = q/{displaymath}rho=epsilon_0,nabla!cdot!{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="\begin{displaymath}
\rho = \epsilon_0  \nabla\!\cdot \!{\bf E},
\end{displaymath}">|; 

$key = q/phi_3=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1414.png"
 ALT="$\phi_3=0$">|; 

$key = q/{displaymath}dot{u}^i=frac{d{u^i}}{dt'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img3230.png"
 ALT="\begin{displaymath}
\dot{u}^i = \frac{d{u^i}}{dt'},
\end{displaymath}">|; 

$key = q/B_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3040.png"
 ALT="$B_x$">|; 

$key = q/2,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1505.png"
 ALT="$2 d$">|; 

$key = q/{displaymath}{{bf{F}=-nablaU+nablatimes{{bf{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="\begin{displaymath}
{\bf F} = -\nabla U +\nabla\times{\bf W}.
\end{displaymath}">|; 

$key = q/{displaymath}z=frac{e,E_0}{m_e,omega^2},sin(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2274.png"
 ALT="\begin{displaymath}
z = \frac{e E_0}{m_e \omega^2} \sin(\omega t).
\end{displaymath}">|; 

$key = q/{displaymath}B_z(x,y)=B_0,cos(k_x,x),cos(k_y,y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2609.png"
 ALT="\begin{displaymath}
B_z(x,y) = B_0 \cos(k_x x) \cos(k_y y),
\end{displaymath}">|; 

$key = q/displaystyleleft(frac{2}{alpha+beta}right)E_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2560.png"
 ALT="$\displaystyle \left(\frac{2}{\alpha+\beta}\right) E_i.$">|; 

$key = q/{displaymath}c,B_{ij}=-partial_i{mitPhi}_j+partial_j{mitPhi}_i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3028.png"
 ALT="\begin{displaymath}
c B_{ij} = -\partial_i {\mit \Phi}_j + \partial_j {\mit \Phi}_i,
\end{displaymath}">|; 

$key = q/B=mu_0,I_2slash2pir;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="$B= \mu_0  I_2/2\pi r$">|; 

$key = q/z=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1519.png"
 ALT="$z= d$">|; 

$key = q/theta_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2492.png"
 ALT="$\theta_r$">|; 

$key = q/{{bf{a}equiv,stackrel{displaystylerightarrow}{PQ},equiv,stackrel{displaystylerightarrow}{SR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="${\bf a}\equiv  \stackrel{\displaystyle \rightarrow}{PQ} \equiv \stackrel{\displaystyle \rightarrow}{SR}$">|; 

$key = q/t>t';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="$t&gt;t'$">|; 

$key = q/{displaymath}C_n=frac{4,phi_0}{n,pi}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1640.png"
 ALT="\begin{displaymath}
C_n = \frac{4 \phi_0}{n  \pi}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{B}simeqfrac{1}{4pi,epsilon_0}frac{left[intpartial{{bf{j}_perpsialt,,dV'right]times{{bf{R}_ast}{c^3R_ast^{~2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="\begin{displaymath}
{\bf B} \simeq \frac{1}{4\pi \epsilon_0} \frac{ \left[ \int...
...partial t  dV'\right]
\times{\bf R}_\ast }{c^3 R_\ast^{&nbsp;2}}.
\end{displaymath}">|; 

$key = q/S,cosalpha_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$S \cos\alpha_y$">|; 

$key = q/H_{parallel,1}=H_{parallel,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2465.png"
 ALT="$H_{\parallel 1} = H_{\parallel 2}$">|; 

$key = q/{displaymath}nablacdot{{bf{A}=v({{bf{r}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="\begin{displaymath}
\nabla \cdot{\bf A} = v({\bf r}).
\end{displaymath}">|; 

$key = q/{displaymath}d=frac{2}{sigma}sqrt{frac{epsilon,epsilon_0}{mu_0}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2403.png"
 ALT="\begin{displaymath}
d = \frac{2}{\sigma}\sqrt{\frac{\epsilon \epsilon_0}{\mu_0}},
\end{displaymath}">|; 

$key = q/{{bf{b}=(1slashsqrt{2},,1slashsqrt{2},,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="${\bf b} = (1/\sqrt{2}, 
1/\sqrt{2},  0)$">|; 

$key = q/J^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2964.png"
 ALT="$J^\mu$">|; 

$key = q/{displaymath}frac{d}{dt}left({{bf{a}times{{bf{b}right)=frac{d{{bf{a}}{dt}times{{bf{b}+{{bf{a}timesfrac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="\begin{displaymath}
\frac{d}{dt}\left({\bf a}\times{\bf b}\right) = \frac{d{\bf a}}{dt}\times{\bf b} + {\bf a}\times
\frac{d{\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/v_1=cslashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2453.png"
 ALT="$v_1=c/n_1$">|; 

$key = q/{displaymath}nablatimes{{bf{A}=left(frac{1}{r}frac{partialA_z}{partialtheta}-fra}-frac{1}{r}frac{partialA_r}{partialtheta}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="468" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="\begin{displaymath}
\nabla\times {\bf A}=\left(\frac{1}{r}\frac{\partial A_z}{\p...
...tial r}-\frac{1}{r}\frac{\partial A_r}{\partial \theta}\right)
\end{displaymath}">|; 

$key = q/{displaymath}T_{ij}=-G_{ij}=epsilon_0,(E_i,E_j-E^2,delta_{ij}slash2)+(B_i,B_j-B^2,delta_{ij}slash2)slashmu_0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2197.png"
 ALT="\begin{displaymath}
T_{ij} = - G_{ij} = \epsilon_0 (E_i E_j-E^2 \delta_{ij}/2) + (B_i B_j-B^2 \delta_{ij}/2)/ \mu_0
\end{displaymath}">|; 

$key = q/x,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2711.png"
 ALT="$x t$">|; 

$key = q/{displaymath}nabla^2phi_3=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1409.png"
 ALT="\begin{displaymath}
\nabla^2\phi_3 = 0
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=1.5in{centerline{epsffile{fig1.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="168" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{figure}
\epsfysize =1.5in
\centerline{\epsffile{fig1.eps}}
\end{figure}">|; 

$key = q/{{bf{a}cdot{{bf{b}=a_x,b_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="${\bf a}\cdot {\bf b} = a_x  b_x$">|; 

$key = q/k^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1612.png"
 ALT="$k^2$">|; 

$key = q/{displaymath}frac{{{bf{E}_{{rm{rad},times{{bf{B}_{{rm{rad}}{mu_0}=epsilon_0,c,E_{{rm{rad}^{,2},frac{{{bf{r}}{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3339.png"
 ALT="\begin{displaymath}
\frac{{\bf E}_{\rm rad} \times{\bf B}_{\rm rad}}{\mu_0}
= \epsilon_0  c E_{\rm rad}^{ 2}  \frac{{\bf r}}{r},
\end{displaymath}">|; 

$key = q/{displaymath}int_{-infty}^{infty}g,frac{partialf}{partialx},dx=left[gfright]_{-it_{-infty}^{infty}f,frac{partialg}{partialx},dx.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} g  \frac{\partial f}{\partial x} d...
...\int_{-\infty}^{\infty}
f \frac{\partial g}{\partial x} dx.
\end{displaymath}">|; 

$key = q/{displaymath}int_Vleft{(nablaphi_3)^2+phi_3nabla^2phi_3right}dV=oint_Sphi_3nablaphi_3cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1412.png"
 ALT="\begin{displaymath}
\int_V \left\{ (\nabla\phi_3)^2 +\phi_3 \nabla^2\phi_3\right\} dV =
\oint_S \phi_3 \nabla \phi_3\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/displaystylea_x,b_x+a_y,b_y+a_z,b_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle a_x  b_x + a_y  b_y + a_z  b_z.$">|; 

$key = q/A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1994.png"
 ALT="$A_i$">|; 

$key = q/(partialhslashpartialy)_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$(\partial h/\partial y)_x$">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{l}=(E_{parallel,A}-E_{parallel,B}),l,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="\begin{displaymath}
\oint_C {\bf E} \cdot d{\bf l} = (E_{\parallel A} - E_{\parallel B} )  l,
\end{displaymath}">|; 

$key = q/{displaymath}sigma(x,y)=-frac{q,d}{2pi,(x^2+y^2+d^2)^{3slash2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1500.png"
 ALT="\begin{displaymath}
\sigma(x,y) = - \frac{q d}{2\pi  (x^2+y^2+d^2)^{3/2}}.
\end{displaymath}">|; 

$key = q/v_p=cslashn=cslashsqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2331.png"
 ALT="$v_p = c/n=c/\sqrt{\epsilon}$">|; 

$key = q/{displaymath}V=-frac{partial}{partialt}oint{{bf{B}cdotd{{bf{S}simfrac{B,A}{t},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="\begin{displaymath}
V = -\frac{\partial}{\partial t} \oint {\bf B}\cdot d{\bf S} \sim \frac{ B A}{t},
\end{displaymath}">|; 

$key = q/{displaymath}g_{mu'nu'},p_{musigma}^{mu'},p_{nu}^{nu'}+g_{mu'nu'},p_{mu}^{mu'},p_{nusigma}^{nu'}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2919.png"
 ALT="\begin{displaymath}
g_{\mu'\nu'} p_{\mu\sigma}^{\mu'}  p_{\nu}^{\nu'} + g_{\mu'\nu'} 
p_{\mu}^{\mu'} p_{\nu\sigma}^{\nu'} = 0,
\end{displaymath}">|; 

$key = q/partial{{bf{E}slashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1938.png"
 ALT="$\partial {\bf E}/\partial t$">|; 

$key = q/{displaymath}{{bf{curl},({{bf{curl},{{bf{A})={{bf{grad},({mitdiv},{{bf{A})-nabla^2{{bf{A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="\begin{displaymath}
{\bf curl} ({\bf curl} {\bf A} ) = {\bf grad} ({\mit div} {\bf A})
- \nabla^2 {\bf A},
\end{displaymath}">|; 

$key = q/d{{bf{l}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1872.png"
 ALT="$d{\bf l}_2 $">|; 

$key = q/I=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1899.png"
 ALT="$I=0$">|; 

$key = q/{{bf{B}_1={{bf{B}_2={{bf{B}_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1456.png"
 ALT="${\bf B}_1={\bf B}_2={\bf B}_S$">|; 

$key = q/10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="$10^{-7}$">|; 

$key = q/B_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2807.png"
 ALT="$B_{ij}$">|; 

$key = q/displaystyle{{bf{B}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2528.png"
 ALT="$\displaystyle {\bf B}_r$">|; 

$key = q/displaystyleepsilon_0,{{bf{E}times(nablatimes{{bf{E})+frac{{{bf{B}times(nablatimes{{bf{B})}{mu_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2180.png"
 ALT="$\displaystyle \epsilon_0 {\bf E}\times (\nabla\times{\bf E})+\frac{{\bf B}\times(\nabla\times {\bf B})}{\mu_0}$">|; 

$key = q/L,deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2042.png"
 ALT="$L \delta x$">|; 

$key = q/{displaymath}J^mu=rho_0,frac{dx^mu}{dtau}=rho_0,U^mu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2961.png"
 ALT="\begin{displaymath}
J^\mu = \rho_0  \frac{dx^\mu}{d\tau} = \rho_0  U^\mu.
\end{displaymath}">|; 

$key = q/{displaymath}H_{parallel,2}-H_{parallel,1}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1810.png"
 ALT="\begin{displaymath}
H_{\parallel 2}-H_{\parallel 1} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}partial_muA^{nusigma}equiv{A^{nusigma}}_{,mu}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2908.png"
 ALT="\begin{displaymath}
\partial_\mu A^{\nu\sigma} \equiv {A^{\nu\sigma}}_{,\mu}.
\end{displaymath}">|; 

$key = q/{displaymath}-(x_2-x_1)^2-(y_2-y_1)^2-(z_2-z_1)^2+c^2(t_2-t_1)^2=s^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2859.png"
 ALT="\begin{displaymath}
-(x_2-x_1)^2- (y_2-y_1)^2 - (z_2-z_1)^2 +c^2(t_2-t_1)^2 = s^2.
\end{displaymath}">|; 

$key = q/{{bf{c}equiv,stackrel{displaystylerightarrow}{PR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="${\bf c} \equiv
 \stackrel{\displaystyle \rightarrow}{PR}$">|; 

$key = q/(A)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2842.png"
 ALT="$(A)^2$">|; 

$key = q/displaystyleoint_{S_i}{{bf{E}_1cdotd{{bf{S}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1429.png"
 ALT="$\displaystyle \oint_{S_i} {\bf E}_1\cdot d{\bf S}_i$">|; 

$key = q/I_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$I_{\rm max}$">|; 

$key = q/{displaymath}nablatimesnablatimes{{bf{E}=-nabla^2{{bf{E}=-frac{partialnablatimesilon_0mu_0,frac{partial{{bf{E}}{partialt}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="516" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2397.png"
 ALT="\begin{displaymath}
\nabla\times\nabla\times{\bf E} = -\nabla^2{\bf E} = -\frac{...
... \epsilon_0\mu_0 \frac{\partial {\bf E}}{\partial t}\right].
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2},LI_T^{,2}+Rint_0^TI^2,dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1950.png"
 ALT="\begin{displaymath}
W = \frac{1}{2}  L I_T^{ 2} + R \int_0^T I^2 dt.
\end{displaymath}">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$B$">|; 

$key = q/{displaymath}R=frac{1}{2}({{rm{retarded})-frac{1}{2}({{rm{advanced}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="\begin{displaymath}
R = \frac{1}{2} ({\rm retarded}) - \frac{1}{2} ({\rm advanced}).
\end{displaymath}">|; 

$key = q/displaystyle+frac{1}{2},L_1,I_1^{,2}+frac{1}{2},L_2,I_2^{,2}+M,I_1,I_2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1964.png"
 ALT="$\displaystyle + \frac{1}{2}  L_1  I_1^{ 2} + \frac{1}{2}  L_2  I_2^{ 2} + M  I_1  I_2.$">|; 

$key = q/{displaymath}{mitDelta}varphi=varphi-varphi_0=frac{e^3}{2,epsilon_0,m_e^{,2},c},frac{1}{omega^2}intn_e(z),B_0(z),dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2390.png"
 ALT="\begin{displaymath}
{\mit\Delta}\varphi = \varphi - \varphi_0=\frac{e^3}{2 \eps...
..._0 m_e^{ 2} c} \frac{1}{\omega^2}
\int n_e(z) B_0(z) dz.
\end{displaymath}">|; 

$key = q/A_{kcdotsl}^{icdotsj};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2824.png"
 ALT="$A_{k\cdots l}^{i\cdots j}$">|; 

$key = q/{displaymath}x'=B,(x-v,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2708.png"
 ALT="\begin{displaymath}
x' = B  (x-v t),
\end{displaymath}">|; 

$key = q/{displaymath}ksimeqn,frac{omega}{c}+{{rm{i},frac{sigma}{2}sqrt{frac{mu_0}{epsilon,epsilon_0}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2401.png"
 ALT="\begin{displaymath}
k\simeq n \frac{\omega}{c} + {\rm i} \frac{\sigma}{2}\sqrt{\frac{\mu_0}
{\epsilon \epsilon_0}},
\end{displaymath}">|; 

$key = q/{{bf{r}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="${\bf r}_2$">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{l}=int_Snablatimes{{bf{B}cdotd{{bf{S}=mu_0,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf l} = \int_S \nabla\times{\bf B} \cdot d{\bf S}
=\mu_0  I.
\end{displaymath}">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$t$">|; 

$key = q/nu';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2924.png"
 ALT="$\nu'$">|; 

$key = q/{figure}{epsfysize{=4in{centerline{epsffile[-300-40860771]{figx9.ps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="443" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="\begin{figure}
\epsfysize =4in
\centerline{\epsffile[-300 -40 860 771]{figx9.ps}}
\end{figure}">|; 

$key = q/x^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2710.png"
 ALT="$x^2$">|; 

$key = q/{displaymath}B^i=g^{ij}B_j.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2839.png"
 ALT="\begin{displaymath}
B^i = g^{ij} B_j.
\end{displaymath}">|; 

$key = q/R_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="$R_\ast$">|; 

$key = q/displaystylenablatimes{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$\displaystyle \nabla\times{\bf E}$">|; 

$key = q/{{bf{j}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="${\bf j}({\bf r})$">|; 

$key = q/{{bf{D}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1761.png"
 ALT="${\bf D}({\bf r})$">|; 

$key = q/{displaymath}W=frac{1}{2}sum_{i=1}^NI_{0,i},{mitPhi}_{0,i}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1987.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \sum_{i=1}^N I_{0 i}  {\mit\Phi}_{0 i}.
\end{displaymath}">|; 

$key = q/U^mu=gamma(u),({{bf{u},c);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3129.png"
 ALT="$U^\mu =\gamma(u) ({\bf u}, c)$">|; 

$key = q/{displaymath}frac{q}{m}=frac{2,d,E}{l^2,B^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="\begin{displaymath}
\frac{q}{m} = \frac{2 d  E}{l^2  B^2}.
\end{displaymath}">|; 

$key = q/{displaymath}C_n=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1639.png"
 ALT="\begin{displaymath}
C_n = 0
\end{displaymath}">|; 

$key = q/displaystyleE_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3094.png"
 ALT="$\displaystyle E_\parallel,$">|; 

$key = q/displaystylefrac{dz'}{dt'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2741.png"
 ALT="$\displaystyle \frac{dz'}{dt'}.$">|; 

$key = q/{displaymath}V(x,t)=V_0cos(omega,t-k,x),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2059.png"
 ALT="\begin{displaymath}
V(x, t) = V_0 \cos(\omega  t - k x),
\end{displaymath}">|; 

$key = q/{{bf{E}rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1728.png"
 ALT="${\bf E}\rightarrow
0$">|; 

$key = q/-partial{{bf{A}slashpartialt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$-\partial {\bf A}/\partial t$">|; 

$key = q/{displaymath}Q=-frac{q,d}{2pi}int_0^inftyfrac{2pi,r,dr}{(r^2+d^2)^{3slash2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1502.png"
 ALT="\begin{displaymath}
Q = - \frac{q d}{2\pi} \int_0^\infty \frac{2\pi  r dr}{(r^2+d^2)^{3/2}},
\end{displaymath}">|; 

$key = q/displaystylefrac{partial^2U}{partialx^2}+frac{partial^2U}{partialy^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1563.png"
 ALT="$\displaystyle \frac{\partial^2 U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2}$">|; 

$key = q/{{bf{B}=B,hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="${\bf B} = B \hat{\bf z}$">|; 

$key = q/{{bf{C}rightarrowmu_0,{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="${\bf C} \rightarrow \mu_0  {\bf j}$">|; 

$key = q/nabla^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="$\nabla^2$">|; 

$key = q/{{bf{E}times{{bf{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1852.png"
 ALT="${\bf E}\times{\bf H}$">|; 

$key = q/[({{bf{E}cdotnabla){{bf{E}]_i=E_j,(partialE_islashpartialx_j);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2190.png"
 ALT="$[({\bf E}\cdot\nabla){\bf E}]_i = E_j (\partial E_i/\partial x_j)$">|; 

$key = q/{displaymath}{{bf{E}simeq-frac{1}{4pi,epsilon_0}frac{left[intpartial{{bf{j}_perpslashpartialt,,dV'right]}{c^2R_ast},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="\begin{displaymath}
{\bf E} \simeq -\frac{1}{4\pi  \epsilon_0} \frac{\left[
\int \partial {\bf j}_\perp/\partial t  dV'\right]}{c^2 R_\ast},
\end{displaymath}">|; 

$key = q/d{{bf{S}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1978.png"
 ALT="$d{\bf S}_i$">|; 

$key = q/dt=dtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2935.png"
 ALT="$dt=d\tau$">|; 

$key = q/{displaymath}frac{4pi}{mu_0,e},{{bf{B}=frac{{{bf{u}times{{bf{r}}{s^3}left(1-frac{r,{{bf{u}}{c}right)timesdot{{bf{u}right]right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3259.png"
 ALT="\begin{displaymath}
\frac{4\pi}{\mu_0 e}  {\bf B} =
\frac{{\bf u}\times{\bf r}...
...
\frac{r {\bf u}}{c}\right)\times\dot{\bf u}\right]
\right).
\end{displaymath}">|; 

$key = q/displaystylex;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle x$">|; 

$key = q/{displaymath}W=frac{Q^2}{8pi,epsilon_0}left(frac{1}{a^6}int_0^ar^4,dr+int_a^inftyfrac{dr}{r^2}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="\begin{displaymath}
W = \frac{Q^2}{8\pi \epsilon_0} \left(
\frac{1}{a^6} \int_0^a r^4 dr + \int_a^\infty \frac{dr}{r^2} \right),
\end{displaymath}">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2847.png"
 ALT="$s$">|; 

$key = q/{displaymath}W=frac{1}{2}sum_{i=1}^NI_ioint{{bf{A}cdotd{{bf{l}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1990.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \sum_{i=1}^N I_i \oint {\bf A} \cdot d{\bf l}_i.
\end{displaymath}">|; 

$key = q/uslashcrightarrow1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3346.png"
 ALT="$u/c\rightarrow 1$">|; 

$key = q/{displaymath}-{{bf{E}cdot{{bf{j}=nabla!cdot!left(frac{{{bf{E}times{{bf{B}}{mu_0}(frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2122.png"
 ALT="\begin{displaymath}
- {\bf E} \cdot {\bf j} = \nabla\! \cdot
\!\left(\frac{{\bf ...
...left( \frac{\epsilon_0 E^2}{2} +\frac{B^2}{2 \mu_0}
\right).
\end{displaymath}">|; 

$key = q/{displaymath}v({{bf{r},t)=intintdelta({{bf{r}-{{bf{r'}),delta(t-t'),v({{bf{r}',t'),d^3{{bf{r}',dt'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="\begin{displaymath}
v({\bf r}, t) = \int\int \delta({\bf r} - {\bf r'})  \delta (t-t') v({\bf r}', t') 
d^3{\bf r}'  dt'.
\end{displaymath}">|; 

$key = q/k_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2384.png"
 ALT="$k_-$">|; 

$key = q/-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3011.png"
 ALT="$-1$">|; 

$key = q/|p_mu^{mu'}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3001.png"
 ALT="$\vert p_\mu^{\mu'}\vert$">|; 

$key = q/{displaymath}p=frac{epsilon_0}{2},E^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="\begin{displaymath}
p = \frac{\epsilon_0}{2}  E^2,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}=a_x,{{bf{e}_x+a_y,{{bf{e}_y+a_z,{{bf{e}_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="\begin{displaymath}
{\bf a} = a_x  {\bf e}_x + a_y  {\bf e}_y + a_z {\bf e}_z.
\end{displaymath}">|; 

$key = q/v({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="$ v({\bf r})$">|; 

$key = q/{displaymath}dtau^2=dt^2left[-frac{dx^2+dy^2+dz^2}{c^2,dt^2}+1right]=dt^2left(1-frac{u^2}{c^2}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2933.png"
 ALT="\begin{displaymath}
d\tau^2 = dt^2\left[ -\frac{dx^2+dy^2+dz^2}{c^2  dt^2} + 1\right]
=dt^2\left(1-\frac{u^2}{c^2}\right),
\end{displaymath}">|; 

$key = q/phistackrel{_{{normalsize{<}}{_{{normalsize{sim}}{mitDelta}theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3395.png"
 ALT="$\phi \stackrel {_{\normalsize &lt;}}{_{\normalsize\sim}}{\mit\Delta}\theta$">|; 

$key = q/displaystyle(nablatimes{{bf{B})_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="$\displaystyle (\nabla\times {\bf B})_z$">|; 

$key = q/(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2697.png"
 ALT="$(x, y, z, t)$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j}+epsilon_0mu_0,frac{partial{{bf{E}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0  {\bf j} + \epsilon_0\mu_0  \frac{\partial {\bf E}}{\partial
t},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{a}=|a|^2=a^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf a} = \vert a\vert^2 = a^2.
\end{displaymath}">|; 

$key = q/{displaymath}phi(r,theta)=-E_0,r,costheta+alpha,r^{-2},costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1652.png"
 ALT="\begin{displaymath}
\phi(r,\theta) = - E_0 r \cos\theta + \alpha r^{-2} \cos\theta.
\end{displaymath}">|; 

$key = q/{displaymath}(A)^2=g_{ij},A^i,A^j=A_i,A^i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2844.png"
 ALT="\begin{displaymath}
(A)^2 = g_{ij}  A^i  A^j = A_i  A^i.
\end{displaymath}">|; 

$key = q/deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="$\delta t$">|; 

$key = q/{displaymath}{{bf{B}({{bf{r})=frac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r}')times({{bfr}-{{bf{r}')}{|{{bf{r}-{{bf{r}'|^3},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="\begin{displaymath}
{\bf B} ({\bf r}) = \frac{\mu_0}{4\pi} \int
\frac{{\bf j}({\...
... r} - {\bf r}')}{\vert{\bf r} - {\bf r}'\vert^3} d^3{\bf r}',
\end{displaymath}">|; 

$key = q/displaystylehat{{bf{n}cdotnablaB_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2603.png"
 ALT="$\displaystyle \hat{\bf n}\cdot\nabla B_z$">|; 

$key = q/gamma^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3402.png"
 ALT="$\gamma^3$">|; 

$key = q/displaystyle-frac{partialE_z}{partialx}+{{rm{i},k,E_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2580.png"
 ALT="$\displaystyle -\frac{\partial E_z}{\partial x} + {\rm i} k E_x,$">|; 

$key = q/{mitDelta}thetasim1slashgamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3394.png"
 ALT="${\mit\Delta}\theta \sim 1/\gamma$">|; 

$key = q/{mitdiv},{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="${\mit div} {\bf A}$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig38.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig38.eps}}
\end{figure}">|; 

$key = q/k_{r,y}=k_{t,y}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2509.png"
 ALT="$k_{r y} =k_{t y}=0$">|; 

$key = q/{displaymath}frac{partialrho}{partialt}+nabla!cdot!{{bf{j}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2966.png"
 ALT="\begin{displaymath}
\frac{\partial\rho}{\partial t} + \nabla\!\cdot\!{\bf j} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}phi(r)=frac{q}{4pi,epsilon_0,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="\begin{displaymath}
\phi( r) = \frac{q}{4\pi \epsilon_0 r}.
\end{displaymath}">|; 

$key = q/rgglambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2217.png"
 ALT="$r\gg \lambda$">|; 

$key = q/n>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2318.png"
 ALT="$n&gt;1$">|; 

$key = q/{displaymath}f_mu=c^{-1},F_{munu}J^nu{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3184.png"
 ALT="\begin{displaymath}
f_\mu = c^{-1}  F_{\mu\nu} J^\nu
\end{displaymath}">|; 

$key = q/displaystylephi({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="$\displaystyle \phi({\bf r})$">|; 

$key = q/{displaymath}nabla=left(frac{partial}{partialx},,frac{partial}{partialy},,frac{partial}{partialz}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="\begin{displaymath}
\nabla = \left(\frac{\partial}{\partial x},  \frac{\partial}{\partial y}, 
\frac{\partial}{\partial z}\right)
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=|a|,|b|,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = \vert a\vert  \vert b\vert  \cos\theta.
\end{displaymath}">|; 

$key = q/displaystyledl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$\displaystyle dl$">|; 

$key = q/-({partial}slash{partialt})(int_Vrho,dV);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$-({\partial}/{\partial t})(\int_V \rho dV)$">|; 

$key = q/{displaymath}W=frac{1}{2,mu_0}int_V{{bf{A}cdotnablatimes{{bf{B},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1996.png"
 ALT="\begin{displaymath}
W = \frac{1}{2 \mu_0} \int_V {\bf A} \cdot \nabla\times{\bf B}   dV.
\end{displaymath}">|; 

$key = q/cos^2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2159.png"
 ALT="$\cos^2 \theta$">|; 

$key = q/{{bf{j}({{bf{r}')=d{{bf{l}_1,I_1slashdl_1,dA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1875.png"
 ALT="${\bf j}({\bf r}') = d{\bf l}_1  I_1/ dl_1  dA$">|; 

$key = q/{displaymath}W=frac{1}{4pi,epsilon_0}sum_{i=1}^Nsum_{j<i}^Nfrac{q_i,q_j}{|{{bf{r}_i-{{bf{r}_j|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="\begin{displaymath}
W = \frac{1}{4\pi \epsilon_0} \sum_{i=1}^N \sum_{j&lt;i}^N\frac{q_i  q_j}{\vert{\bf r}_i
-{\bf r}_j\vert}.
\end{displaymath}">|; 

$key = q/g_{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2868.png"
 ALT="$g_{\mu \nu}$">|; 

$key = q/{{bf{F};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="${\bf F}$">|; 

$key = q/q_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$q_1$">|; 

$key = q/P=(0,0,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2685.png"
 ALT="$P=(0,0,0,0)$">|; 

$key = q/dsproptodtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2942.png"
 ALT="$ds\propto d\tau$">|; 

$key = q/I_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1928.png"
 ALT="$I_2=0$">|; 

$key = q/displaystyleB_{perp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2601.png"
 ALT="$\displaystyle B_{\perp}$">|; 

$key = q/Deltat'<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2768.png"
 ALT="$\Delta t'&lt;0$">|; 

$key = q/displaystyleintintintz,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle \int\int
\int z dV$">|; 

$key = q/V(Q);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$V(Q)$">|; 

$key = q/displaystyleds^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2863.png"
 ALT="$\displaystyle ds^2$">|; 

$key = q/phi_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1408.png"
 ALT="$\phi_3$">|; 

$key = q/nablatimes{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$\nabla\times {\bf B} $">|; 

$key = q/displaystyleA_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="$\displaystyle A_x$">|; 

$key = q/delta_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2191.png"
 ALT="$\delta_{ij}$">|; 

$key = q/R_0sim30,000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="$R_0 \sim 30,000$">|; 

$key = q/{displaymath}t_a=t+|{{bf{r}-{{bf{r}'|slashc.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="\begin{displaymath}
t_a = t + \vert{\bf r} - {\bf r}'\vert/c.
\end{displaymath}">|; 

$key = q/10^{-11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="$10^{-11}$">|; 

$key = q/{displaymath}G({{bf{r},{{bf{r}';t,t')=frac{F(t-t'-|{{bf{r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="\begin{displaymath}
G({\bf r}, {\bf r}'; t, t') = \frac{F(t-t' - \vert{\bf r} - {\bf r}'\vert/c)}{\vert{\bf r} - {\bf r}'\vert},
\end{displaymath}">|; 

$key = q/{displaymath}V=E_perp,d=frac{sigma,d}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="\begin{displaymath}
V = E_\perp d = \frac{\sigma  d}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/displaystyley;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle y$">|; 

$key = q/{{bf{r}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="${\bf r}_0$">|; 

$key = q/displaystylefrac{1}{z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1538.png"
 ALT="$\displaystyle \frac{1}{z}.$">|; 

$key = q/omega<10^9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2418.png"
 ALT="$\omega &lt; 10^9$">|; 

$key = q/displaystylefrac{partialU}{partialx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1557.png"
 ALT="$\displaystyle \frac{\partial U}{\partial x}$">|; 

$key = q/{{bf{H}_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1806.png"
 ALT="${\bf H}_{\rm max}$">|; 

$key = q/n_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2324.png"
 ALT="$n_e$">|; 

$key = q/E_1<E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1745.png"
 ALT="$E_1 &lt; E_0$">|; 

$key = q/{displaymath}P={{bf{j}cdot{{bf{E}=sigma,E^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2410.png"
 ALT="\begin{displaymath}
P = {\bf j}\cdot{\bf E} = \sigma E^2.
\end{displaymath}">|; 

$key = q/theta<pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3344.png"
 ALT="$\theta &lt;\pi/2$">|; 

$key = q/V_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1920.png"
 ALT="$V_1$">|; 

$key = q/displaystylegamma^3,a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3152.png"
 ALT="$\displaystyle \gamma^3  a,$">|; 

$key = q/{displaymath}V=int_{x_1}^{x_2}dxint_{y_1(x)}^{y_2(x)}D(x,y),dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="\begin{displaymath}
V = \int_{x_1}^{x_2} dx \int_{y_1(x)}^{y_2(x)} D(x,y) dy.
\end{displaymath}">|; 

$key = q/displaystyle-int_{{rm{outer}^{{rm{inner}{{bf{E}cdotd{{bf{l}=int_{{rm{inner}^{{rm{outer}{{bf{E}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1391.png"
 ALT="$\displaystyle - \int_{\rm outer}^{\rm inner} {\bf E} \cdot d{\bf l} =
\int_{\rm inner}^{\rm outer}{\bf E} \cdot d{\bf l}$">|; 

$key = q/{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="${\bf r}'$">|; 

$key = q/g_{munu}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2871.png"
 ALT="$g_{\mu\nu}=0$">|; 

$key = q/G_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2170.png"
 ALT="$G_{ij}$">|; 

$key = q/{displaymath}nabla!cdot!({{bf{E}times{{bf{H})equiv{{bf{H}!cdot!(nablatimes{{bf{E})-{{bf{E}!cdot!(nablatimes{{bf{H}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1850.png"
 ALT="\begin{displaymath}
\nabla\!\cdot\!({\bf E}\times{\bf H}) \equiv {\bf H}\!\cdot\!(\nabla\times
{\bf E}) - {\bf E}\!\cdot\!(\nabla\times{\bf H}).
\end{displaymath}">|; 

$key = q/[J^mu],dVslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2998.png"
 ALT="$[J^\mu] dV/r$">|; 

$key = q/{displaymath}{mitDelta}omega=gamma^3,omega_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img3401.png"
 ALT="\begin{displaymath}
{\mit\Delta}\omega = \gamma^3 \omega_0.
\end{displaymath}">|; 

$key = q/displaystyleT^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2883.png"
 ALT="$\displaystyle T^2,$">|; 

$key = q/{displaymath}frac{dt}{dtau}=gamma(u).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2934.png"
 ALT="\begin{displaymath}
\frac{dt}{d\tau} = \gamma(u).
\end{displaymath}">|; 

$key = q/H_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1836.png"
 ALT="$H_g$">|; 

$key = q/rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="$r\rightarrow \infty$">|; 

$key = q/nabla^2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1651.png"
 ALT="$\nabla^2\phi$">|; 

$key = q/q^4slashm^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2297.png"
 ALT="$q^4/m^2$">|; 

$key = q/sigmallepsilon,epsilon_0,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2400.png"
 ALT="$\sigma\ll \epsilon \epsilon_0 \omega$">|; 

$key = q/{displaymath}nabla^2f=frac{1}{r^2}frac{partial}{partialr}!left(r^2frac{partialf}1}{r^2,sin^2theta}frac{partial^2f}{partialphi^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="\begin{displaymath}
\nabla^2 f = \frac{1}{r^2}\frac{\partial}{\partial r}\!\left...
...\frac{1}{r^2 \sin^2\theta}\frac{\partial^2 f}{\partial\phi^2}
\end{displaymath}">|; 

$key = q/theta=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2227.png"
 ALT="$\theta = \pi/2$">|; 

$key = q/-{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2425.png"
 ALT="$-{\bf v}$">|; 

$key = q/displaystyle-epsilon_0,E^iE^j-frac{B^iB^j}{mu_0}+delta^{ij},frac{1}{2}!left(epsilon_0,E^2+frac{B^2}{mu_0}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3207.png"
 ALT="$\displaystyle -\epsilon_0  E^i E^j - \frac{B^i B^j}{\mu_0}
+\delta^{ij} \frac{1}{2} \!\left(\epsilon_0  E^2 +\frac{B^2}{\mu_0}\right),$">|; 

$key = q/Q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1422.png"
 ALT="$Q_i$">|; 

$key = q/x^{4'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3288.png"
 ALT="$x^{4'}$">|; 

$key = q/dsigmaslashd{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2281.png"
 ALT="$d\sigma/d{\mit\Omega}$">|; 

$key = q/-I(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2046.png"
 ALT="$-I(x, t)$">|; 

$key = q/u'<c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2759.png"
 ALT="$u'&lt;c$">|; 

$key = q/{displaymath}Q_{{rm{total}=sum_{i=1}^NQ_i+int_Vrho,dV{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1437.png"
 ALT="\begin{displaymath}
Q_{\rm total} = \sum_{i=1}^N Q_i + \int_V \rho dV
\end{displaymath}">|; 

$key = q/{displaymath}p_{i'}^i,p_j^{i'}=delta_j^i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2786.png"
 ALT="\begin{displaymath}
p_{i'}^i  p_j^{i'} = \delta_j^i,
\end{displaymath}">|; 

$key = q/{displaymath}frac{partialU}{partialt}+nablacdot{{bf{u}=-{{bf{E}cdot{{bf{j},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2123.png"
 ALT="\begin{displaymath}
\frac{\partial U}{\partial t} + \nabla\cdot{\bf u} = -{\bf E}\cdot {\bf j},
\end{displaymath}">|; 

$key = q/{displaymath}v=frac{E}{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="\begin{displaymath}
v = \frac{E}{B}.
\end{displaymath}">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$\phi$">|; 

$key = q/displaystylefrac{partialB_x}{partialx}+frac{partialB_y}{partialy}+{{rm{i},k,B_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2576.png"
 ALT="$\displaystyle \frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y} + {\rm i} k B_z$">|; 

$key = q/{displaymath}frac{E_i-E_r}{v_1}=frac{E_t}{v_2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2469.png"
 ALT="\begin{displaymath}
\frac{E_i - E_r}{v_1} = \frac{E_t}{v_2},
\end{displaymath}">|; 

$key = q/{displaymath}F(x+{{rm{i},y)=(x+{{rm{i},y)^2=(x^2-y^2)+2,{{rm{i},x,y,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1542.png"
 ALT="\begin{displaymath}
F(x + {\rm i} y) = (x+{\rm i} y)^2 = (x^2-y^2) + 2 {\rm i}  x y,
\end{displaymath}">|; 

$key = q/{displaymath}E_{perp,A}-E_{perp,B}=frac{sigma}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="\begin{displaymath}
E_{\perp A} - E_{\perp  B} = \frac{\sigma}{\epsilon_0}
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E}(z>0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1511.png"
 ALT="$\displaystyle {\bf E} (z&gt;0)$">|; 

$key = q/{displaymath}{{bf{A}_1({{bf{r})=frac{mu_0,I_1}{4pi}oint_{{rm{loop,1}frac{d{{bf{l}_1}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1873.png"
 ALT="\begin{displaymath}
{\bf A}_1 ({\bf r}) = \frac{\mu_0  I_1}{4\pi}
\oint_{\rm loop  1} \frac{d {\bf l}_1}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$\mu_0$">|; 

$key = q/rho({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="$\rho({\bf r}, t)$">|; 

$key = q/E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2596.png"
 ALT="$E_z$">|; 

$key = q/{displaymath}frac{1}{2},partial_j(c,B^{ij}-c,B^{ji})+partial_4F^{4i}=partial_jF^{ji}+partial_4F^{4i}=frac{J^i}{c,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3052.png"
 ALT="\begin{displaymath}
\frac{1}{2} \partial_j(c  B^{ij} - c  B^{ji}) +\partial_4...
...rtial_j F^{ji} +\partial_4 F^{4i}
=\frac{J^i}{c \epsilon_0}.
\end{displaymath}">|; 

$key = q/omega_0=e,Bslashm_0,gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3388.png"
 ALT="$\omega_0 = e  B/ m_0 \gamma$">|; 

$key = q/displaystylea_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle a_{x'}$">|; 

$key = q/{displaymath}phi_{i'}=frac{partialphi}{partialx^{i'}}=frac{partialphi}{partialx^}frac{partialx^i}{partialx^{i'}}=phi_i,p_{i'}^i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2804.png"
 ALT="\begin{displaymath}
\phi_{i'} = \frac{\partial\phi}{\partial x^{i'}} =
\frac{\pa...
... x^i} \frac{\partial x^i}{\partial x^{i'}}
=\phi_i  p_{i'}^i.
\end{displaymath}">|; 

$key = q/{{bf{a}cdot{{bf{b}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="${\bf a} \cdot {\bf b} =0$">|; 

$key = q/int{{bf{A}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$\int {\bf A}\cdot d{\bf l}$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho({\bf r}')}
{\vert{\bf r} - {\bf r}'\vert} d^3{\bf r}'
\end{displaymath}">|; 

$key = q/N_2ggN_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1940.png"
 ALT="$N_2 \gg N_1$">|; 

$key = q/sin^2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2308.png"
 ALT="$\sin^2\theta$">|; 

$key = q/displaystyleT^{1'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2880.png"
 ALT="$\displaystyle T^{1'}$">|; 

$key = q/(0,0,pm1,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2677.png"
 ALT="$(0, 0, \pm 1, 1)$">|; 

$key = q/displaystyle|V_0|,|I_0|int_{omegat=0}^{omegat=2pi}cos(omega,t)left[cos(omega,t),costheta+sin(omega,t),sinthetaright],,frac{d(omega,t)}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2019.png"
 ALT="$\displaystyle \vert V_0\vert  \vert I_0\vert \int_{\omega t =0}^{\omega t = 2\...
...s\theta + \sin(\omega  t)  \sin \theta\right]  
\frac{d(\omega  t)}{2\pi},$">|; 

$key = q/{{bf{a}=(1,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="${\bf a} = (1, 0, 0)$">|; 

$key = q/{displaymath}c,B^i=frac{1}{2},epsilon^{ijk},c,B_{jk}=-epsilon^{ijk},partial_j{mitPhi}_k.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3024.png"
 ALT="\begin{displaymath}
c B^i = \frac{1}{2} \epsilon^{ijk}  c B_{jk} = -\epsilon^{ijk} \partial_j {\mit \Phi}_k.
\end{displaymath}">|; 

$key = q/dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2664.png"
 ALT="$dt'$">|; 

$key = q/displaystyle(,[a_x,c_x+a_y,c_y],b_x,,0,,0)-(a_x,b_x,c_x,,a_x,b_x,c_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle ( [a_x  c_x + a_y  c_y]  b_x,  0,  0) - (a_x  b_x  c_x,  a_x  b_x  c_y,  0)$">|; 

$key = q/{{bf{v}=(v,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2754.png"
 ALT="${\bf v} = (v, 0, 0)$">|; 

$key = q/{displaymath}nabla^2u({{bf{r})=intleft[nabla^2G({{bf{r},,{{bf{r}')right],v({{bf{r}-{{bf{r}'),v({{bf{r}'),d^3{{bf{r}'=v({{bf{r}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="\begin{displaymath}
\nabla^2 u({\bf r}) = \int \left[\nabla^2
G({\bf r},  {\bf...
...a({\bf r} - {\bf r}') v({\bf r}') d^3 {\bf r}' = v({\bf r}).
\end{displaymath}">|; 

$key = q/{{bf{grad},T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="${\bf grad} T$">|; 

$key = q/{displaymath}E_perp=frac{sigma}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1496.png"
 ALT="\begin{displaymath}
E_\perp = \frac{\sigma}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/{mitdiv},{{bf{A}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="${\mit div} {\bf A}\neq 0 $">|; 

$key = q/z<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1493.png"
 ALT="$z&lt;0$">|; 

$key = q/nablaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="$\nabla\phi$">|; 

$key = q/{displaymath}f^mu=left(rho,{{bf{E}+{{bf{j}times{{bf{B},frac{{{bf{E}!cdot!{{bf{j}}{c}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3187.png"
 ALT="\begin{displaymath}
f^\mu = \left( \rho {\bf E} + {\bf j}\times{\bf B}, \frac{{\bf E}\!\cdot
\!{\bf j}}{c}\right).
\end{displaymath}">|; 

$key = q/displaystylemu_0left({{bf{j}+epsilon_0,frac{partial{{bf{E}}{partialt}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3047.png"
 ALT="$\displaystyle \mu_0 \left({\bf j} + \epsilon_0  \frac{\partial
{\bf E}}
{\partial t}\right).$">|; 

$key = q/{displaymath}deltaW=int{{bf{H}!cdot!delta{{bf{B},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1857.png"
 ALT="\begin{displaymath}
\delta W = \int {\bf H}\!\cdot\!\delta {\bf B} d^3{\bf r}.
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2G({{bf{r},{{bf{r}')=delta({{bf{r}-{{bf{r}'){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="\begin{displaymath}
\nabla^2 G({\bf r}, {\bf r}') = \delta({\bf r} - {\bf r}')
\end{displaymath}">|; 

$key = q/{bf{S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\bf S$">|; 

$key = q/displaystyleleft(frac{n_1-n_2}{n_1+n_2}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2486.png"
 ALT="$\displaystyle \left(\frac{n_1-n_2}{n_1+n_2}\right)^2,$">|; 

$key = q/t_r=t-Rslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$t_r = t- R/c$">|; 

$key = q/{displaymath}W=frac{1}{2},C,V^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="\begin{displaymath}
W= \frac{1}{2}  C  V^2.
\end{displaymath}">|; 

$key = q/{displaymath}frac{dp}{dt}=m_0,gamma^3,dot{u},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3321.png"
 ALT="\begin{displaymath}
\frac{d p}{dt} = m_0  \gamma^3 \dot{u},
\end{displaymath}">|; 

$key = q/{displaymath}frac{dx^{i'}}{ds}=frac{partialx^{i'}}{partialx^i}frac{dx^i}{ds}=frac{dx^i}{ds},p_i^{i'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2849.png"
 ALT="\begin{displaymath}
\frac{dx^{i'}}{ds} = \frac{\partial x^{i'}}{\partial x^i}
\frac{d x^i}{ds} = \frac{dx^i}{ds}  p_i^{i'}.
\end{displaymath}">|; 

$key = q/displaystylephi+frac{partialpsi}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$\displaystyle \phi +\frac{\partial \psi}{\partial t},$">|; 

$key = q/{displaymath}partial_muF^{munu}=frac{J^nu}{c,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img3053.png"
 ALT="\begin{displaymath}
\partial_\mu F^{\mu\nu} = \frac{J^\nu}{c \epsilon_0}.
\end{displaymath}">|; 

$key = q/E_rslashE_i<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2479.png"
 ALT="$E_r/E_i&lt;0$">|; 

$key = q/A_muU^mu=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3181.png"
 ALT="$A_\mu U^\mu =0$">|; 

$key = q/displaystylec,A_2'=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3112.png"
 ALT="$\displaystyle c A_2' = 0,$">|; 

$key = q/{displaymath}u^i=frac{d{x^i}'}{dt'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3229.png"
 ALT="\begin{displaymath}
u^i = \frac{d{x^i}'}{dt'},
\end{displaymath}">|; 

$key = q/{displaymath}q-q'=q''.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1716.png"
 ALT="\begin{displaymath}
q-q' = q''.
\end{displaymath}">|; 

$key = q/displaystyleint_0^T(V_1,I_1+V_2,I_2),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1960.png"
 ALT="$\displaystyle \int_0^T (V_1  I_1 + V_2  I_2 ) dt$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="$E$">|; 

$key = q/{displaymath}nablacdot{{bf{B}=frac{mu_0,I}{2pi}left(frac{2,y,x}{r^4}-frac{2,x,y}{r^4}right)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf B} = \frac{\mu_0  I}{2\pi}\left( \frac{2 y x}{r^4}-\frac{2 x y}{r^4}
\right) = 0,
\end{displaymath}">|; 

$key = q/displaystyle(nablatimes{{bf{A})_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="$\displaystyle (\nabla\times{\bf A})_x$">|; 

$key = q/k=omegaslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2060.png"
 ALT="$k= \omega / v$">|; 

$key = q/displaystyleepsilon_1,E_z(z=0^+);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1698.png"
 ALT="$\displaystyle \epsilon_1  E_z(z=0^+)$">|; 

$key = q/{displaymath}int_S{{bf{E}cdotd{{bf{S}=int_Vnablacdot{{bf{E},,d^3{{bf{r}=frac{Q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="\begin{displaymath}
\int_S {\bf E}\cdot d{\bf S} = \int_V \nabla\cdot{\bf E}  
d^3{\bf r}= \frac{Q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}_2=frac{mu_0,I_1}{4pi}oint_{{rm{loop,1}oint_{{rm{loop,2}frac{d{{bf{l}_1cdotd{{bf{l}_2}{|{{bf{r}-{{bf{r}'|},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1878.png"
 ALT="\begin{displaymath}
{\mit\Phi}_2 = \frac{\mu_0  I_1}{4\pi}
\oint_{\rm loop  1...
...frac{d{\bf l}_1\cdot d{\bf l}_2}{\vert{\bf r}-
{\bf r}'\vert},
\end{displaymath}">|; 

$key = q/R=sqrt{LslashR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2064.png"
 ALT="$R= \sqrt{L/R}$">|; 

$key = q/displaystylefrac{partialx^i}{partialx^{i'}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2784.png"
 ALT="$\displaystyle \frac{\partial x^i}{\partial x^{i'}}$">|; 

$key = q/displaystyleE_r,{{rm{e}^{,{{rm{i},(-k_1,z-omega,t)},hat{{bf{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2455.png"
 ALT="$\displaystyle E_r {\rm e}^{ {\rm i} (-k_1 z-\omega t)} \hat{\bf x},$">|; 

$key = q/displaystylehat{{bf{k}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2516.png"
 ALT="$\displaystyle \hat{\bf k}_i$">|; 

$key = q/n=0,1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2616.png"
 ALT="$n=0, 1, 2, \cdots$">|; 

$key = q/{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="${\bf c}$">|; 

$key = q/V(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1574.png"
 ALT="$V(x,y)$">|; 

$key = q/m_psim10^{-27},{{rm{kg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2291.png"
 ALT="$m_p\sim 10^{-27} {\rm kg}$">|; 

$key = q/{displaymath}epsilon_{iab},epsilon^{ijk}=delta_a^j,delta_b^k-delta_b^j,delta_a^k.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3026.png"
 ALT="\begin{displaymath}
\epsilon_{iab}  \epsilon^{ijk} = \delta_a^j  \delta_b^k - \delta_b^j \delta_a^k.
\end{displaymath}">|; 

$key = q/N_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1910.png"
 ALT="$N_2$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=left(frac{partialA_y}{partialx}-frac{partialA_x}{partialy}right)dS_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="\begin{displaymath}
\oint {\bf A} \cdot d{\bf l} = \left(\frac{\partial A_y}{\partial x}-
\frac{\partial A_x}{\partial y}\right) dS_z.
\end{displaymath}">|; 

$key = q/displaystyleE_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle E_\perp$">|; 

$key = q/{displaymath}Z_{{rm{in}={{rm{i},Z_0tan(k,l).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2087.png"
 ALT="\begin{displaymath}
Z_{\rm in} = {\rm i}  Z_0 \tan (k l).
\end{displaymath}">|; 

$key = q/displaystylex-v,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2654.png"
 ALT="$\displaystyle x - v t,$">|; 

$key = q/{displaymath}E^2=p^2c^2+m^2c^4{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2143.png"
 ALT="\begin{displaymath}
E^2 = p^2 c^2 + m^2 c^4
\end{displaymath}">|; 

$key = q/R_{{rm{rad}llR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2240.png"
 ALT="$R_{\rm rad} \ll R$">|; 

$key = q/y=0,b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2608.png"
 ALT="$y=0, b$">|; 

$key = q/{displaymath}k^2=epsilon_0mu_0,omega^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="\begin{displaymath}
k^2 = \epsilon_0 \mu_0  \omega^2,
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=1.75in{centerline{epsffile{fig20.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="509" HEIGHT="198" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="\begin{figure}
\epsfysize =1.75in
\centerline{\epsffile{fig20.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{partialP_{{rm{load}}{partialR_{{rm{load}}=frac{V_0^{,2}}{2}lefrm{load}}{(R_{{rm{rad}+R_{{rm{load})^3}right]=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2251.png"
 ALT="\begin{displaymath}
\frac{\partial P_{\rm load}}{\partial R_{\rm load}} = \frac{...
...d} - R_{\rm load}}{(R_{\rm rad} + R_{\rm load})^3}\right] = 0.
\end{displaymath}">|; 

$key = q/displaystylefrac{dgamma}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3153.png"
 ALT="$\displaystyle \frac{d\gamma}{dt}$">|; 

$key = q/dt'=gamma,(dt-v,dxslashc^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2745.png"
 ALT="$dt'=
\gamma (dt-v dx/c^2)$">|; 

$key = q/m=-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1735.png"
 ALT="$m=-2$">|; 

$key = q/{displaymath}partial_mu{mitPhi}^mu=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2978.png"
 ALT="\begin{displaymath}
\partial_\mu {\mit \Phi}^\mu =0.
\end{displaymath}">|; 

$key = q/{displaymath}partial_muG^{munu}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3088.png"
 ALT="\begin{displaymath}
\partial_\mu G^{\mu\nu} = 0.
\end{displaymath}">|; 

$key = q/-e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2271.png"
 ALT="$-e$">|; 

$key = q/{displaymath}-dx^2-dy^2-dz^2+c^2,dt^2=ds^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2858.png"
 ALT="\begin{displaymath}
-dx^2 -dy^2-dz^2 +c^2  dt^2 =ds^2,
\end{displaymath}">|; 

$key = q/{displaymath}frac{E_b}{E_a}simeqfrac{a}{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1383.png"
 ALT="\begin{displaymath}
\frac{E_b}{E_a}\simeq \frac{a}{b}.
\end{displaymath}">|; 

$key = q/(0,pm1,0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2676.png"
 ALT="$(0,\pm 1, 0, 1)$">|; 

$key = q/{displaymath}x'=F(x,y,z,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2669.png"
 ALT="\begin{displaymath}
x' = F(x, y, z, t),
\end{displaymath}">|; 

$key = q/cos^{-1}(cslashv);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$\cos^{-1}(c/v)$">|; 

$key = q/displaystyleepsilon_2,E_{perp,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2497.png"
 ALT="$\displaystyle \epsilon_2 E_{\perp 2},$">|; 

$key = q/{{bf{P};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1657.png"
 ALT="${\bf P}$">|; 

$key = q/-q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="$-q$">|; 

$key = q/{displaymath}u({{bf{r},t)=intintG({{bf{r},{{bf{r}';t,t'),v({{bf{r}',t'),d^3{{bf{r}',dt'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="\begin{displaymath}
u({\bf r}, t) = \int\int G({\bf r}, {\bf r}'; t, t') v({\bf r}', t') 
d^3{\bf r}' dt'.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{A}({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="$\displaystyle {\bf A}({\bf r}, t)$">|; 

$key = q/displaystyleE_x(z=0^-),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1701.png"
 ALT="$\displaystyle E_x (z=0^-),$">|; 

$key = q/displaystylec^{-1},nablaphitimeshat{{bf{z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2640.png"
 ALT="$\displaystyle c^{-1} \nabla\phi\times\hat{\bf z},$">|; 

$key = q/lambdasim2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2419.png"
 ALT="$\lambda\sim 2$">|; 

$key = q/displaystyle{{rm{i},frac{omega}{c^2},E_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2585.png"
 ALT="$\displaystyle {\rm i} \frac{\omega}{c^2} E_y$">|; 

$key = q/{{bf{A}_3={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1461.png"
 ALT="${\bf A}_3={\bf0}$">|; 

$key = q/{displaymath}frac{dF}{dz}=~_{lim|deltaz|rightarrowinfty}frac{F(z+deltaz)-F(z)}{deltaz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1547.png"
 ALT="\begin{displaymath}
\frac{dF}{dz} =&nbsp;_{\lim \vert\delta z\vert\rightarrow\infty}
\frac{F(z+\delta z) - F(z) }{\delta z}.
\end{displaymath}">|; 

$key = q/displaystylefrac{partial^2G}{partialx^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="$\displaystyle \frac{\partial^2 G}{\partial x^2}$">|; 

$key = q/-y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$-y$">|; 

$key = q/{{bf{e}_xequiv(1,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="${\bf e}_x \equiv (1,0,0)$">|; 

$key = q/-1.7times10^{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="$-1.7\times 10^{11}$">|; 

$key = q/displaystylefrac{u'_1+v}{1+u'_1,vslashc^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2750.png"
 ALT="$\displaystyle \frac{u'_1+v}{1+u'_1  v/c^2},$">|; 

$key = q/D=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1623.png"
 ALT="$D=0$">|; 

$key = q/displaystylea,dx^2+b,dy^2+c,dz^2+d,dt^2+g,dx,dt+h,dy,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2672.png"
 ALT="$\displaystyle a  dx^2 + b  dy^2 + c  dz^2 + d  dt^2
+ g  dx  dt + h  dy  dt$">|; 

$key = q/displaystylefrac{partialV}{partialx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1559.png"
 ALT="$\displaystyle \frac{\partial V}{\partial x}$">|; 

$key = q/{displaymath}v_g=frac{domega}{dk}=c,sqrt{1-omega_{mn}^{,2}slashomega^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2630.png"
 ALT="\begin{displaymath}
v_g = \frac{d\omega}{d k} = c \sqrt{1-\omega_{mn}^{ 2}/\omega^2},
\end{displaymath}">|; 

$key = q/nablacdot{{bf{P}=epsilon_0,chi_e,nabla{cdot}{{bf{E}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1724.png"
 ALT="$\nabla \cdot {\bf P} = \epsilon_0 
\chi_e  \nabla {\cdot} {\bf E} = 0$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \frac{1}{4\pi \epsilon_0} \int\frac{\rho({\bf r'})}{\vert{\bf r} - {\bf r'}\vert} 
d^3{\bf r'}
\end{displaymath}">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)phi=-frac{rho}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="\begin{displaymath}
\left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2 }{\partial t^2}\right) \phi = -\frac{\rho}
{\epsilon_0}.
\end{displaymath}">|; 

$key = q/deltaE_{{rm{max}sim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3336.png"
 ALT="$\delta E_{\rm max}\sim 1$">|; 

$key = q/{displaymath}{{rm{i},{{bf{k}times{{bf{E}_0={{rm{i},omega,{{bf{B}_0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="\begin{displaymath}
{\rm i} {\bf k}\times {\bf E}_0 = {\rm i}  \omega  {\bf B}_0,
\end{displaymath}">|; 

$key = q/(nablaphi_3)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1416.png"
 ALT="$(\nabla \phi_3)^2$">|; 

$key = q/displaystylefrac{dF}{dz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1551.png"
 ALT="$\displaystyle \frac{dF}{dz}$">|; 

$key = q/{displaymath}int_P^QdT=int_P^Q{{bf{grad},Tcdotd{{bf{l}=T(Q)-T(P).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="\begin{displaymath}
\int_P^Q dT = \int_P^Q {\bf grad} T\cdot d{\bf l} = T(Q)-T(P).
\end{displaymath}">|; 

$key = q/displaystylefrac{Q'}{Q_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1379.png"
 ALT="$\displaystyle \frac{Q'}{Q_0}$">|; 

$key = q/I(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2045.png"
 ALT="$I(x, t)$">|; 

$key = q/{displaymath}{{bf{A}({{bf{r},t)=frac{mu_0}{4pi}intfrac{[{{bf{j}]}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2203.png"
 ALT="\begin{displaymath}
{\bf A}({\bf r}, t) = \frac{\mu_0}{4\pi} \int \frac{[{\bf j}]}{\vert{\bf r} - {\bf r}'\vert} 
d^3{\bf r}',
\end{displaymath}">|; 

$key = q/{displaymath}[{{bf{r}times({{bf{r}_utimesdot{{bf{u})]^2=-({{bf{r}!cdot!dot{{bf{udot{u}^2,r^4,(1-{{bf{r}!cdot!{{bf{u}slashr,c)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="499" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3367.png"
 ALT="\begin{displaymath}[{\bf r}\times({\bf r}_u\times \dot{\bf u})]^2 =
-({\bf r}\!...
...^2/c^2)
+\dot{u}^2  r^4  (1-{\bf r}\!\cdot\!{\bf u}/r c)^2,
\end{displaymath}">|; 

$key = q/{displaymath}frac{sintheta_t}{sintheta_i}=frac{v_2}{v_1}=frac{n_1}{n_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2515.png"
 ALT="\begin{displaymath}
\frac{\sin\theta_t}{\sin\theta_i} = \frac{v_2}{v_1} = \frac{n_1}{n_2}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig36.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="673" HEIGHT="284" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig36.eps}}
\end{figure}">|; 

$key = q/{{bf{B}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="${\bf B}_1$">|; 

$key = q/{{bf{H}=-nablaphi_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1815.png"
 ALT="${\bf H} = -\nabla\phi_m$">|; 

$key = q/{{bf{B}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2503.png"
 ALT="${\bf B}_r$">|; 

$key = q/langle{{bf{p}_irangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1660.png"
 ALT="$\langle {\bf p}_i\rangle$">|; 

$key = q/t-|{{bf{r}-{{bf{r}'|slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="$t-\vert{\bf r} - {\bf r}'\vert/c$">|; 

$key = q/displaystyle-frac{partial}{partialt}left[epsilon_0,{{bf{E}times{{bf{B}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2179.png"
 ALT="$\displaystyle -\frac{\partial}{\partial t} \left[\epsilon_0 {\bf E}\times{\bf B}\right]$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$V$">|; 

$key = q/nabla^2phi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1420.png"
 ALT="$\nabla^2 \phi
=0 $">|; 

$key = q/{displaymath}langlePrangle=frac{1}{2}int_{0}^inftysigma,E_0^{,2},e^{-2,zslashd},0^{,2}=sqrt{frac{sigma}{8,mu_0,omega}},E_0^{,2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2411.png"
 ALT="\begin{displaymath}
\langle P\rangle = \frac{1}{2}\int_{0}^\infty
\sigma E_0^{\...
...E_0^{ 2} =
\sqrt{\frac{\sigma}{8 \mu_0 \omega}} E_0^{ 2},
\end{displaymath}">|; 

$key = q/{displaymath}G({{bf{r},{{bf{r}';t,t')=-frac{1}{4pi}frac{delta(t-t'-|{{bf{r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="\begin{displaymath}
G({\bf r}, {\bf r}'; t, t') = -\frac{1}{4\pi} \frac{\delta(t...
...vert{\bf r} - {\bf r}'\vert/c)}
{\vert{\bf r} - {\bf r}'\vert}
\end{displaymath}">|; 

$key = q/psi({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2976.png"
 ALT="$\psi({\bf r}, t)$">|; 

$key = q/displaystyle-frac{mu_0,e}{4pi}frac{gamma}{r^3,(1+u_r^{~2},gamma^2slashc^2)^{3slash2}},{{bf{u}times{{bf{r}=frac{1}{c^2},{{bf{u}times{{bf{E}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3142.png"
 ALT="$\displaystyle - \frac{\mu_0 e}{4\pi} \frac{\gamma}{r^3 
(1+u_r^{&nbsp;2}  \gamma^2/c^2)^{3/2}}  {\bf u}\times{\bf r}
= \frac{1}{c^2}  {\bf u}\times{\bf E}.$">|; 

$key = q/{displaymath}nablacdot{{bf{j}+frac{partialrho}{partialt}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf j} +\frac{\partial\rho}{\partial t} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}frac{d}{dt}left({{bf{a}cdot{{bf{b}right)=frac{d{{bf{a}}{dt}cdot{{bf{b}+{{bf{a}cdotfrac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="\begin{displaymath}
\frac{d}{dt}\left({\bf a}\cdot{\bf b}\right) = \frac{d{\bf a}}{dt}\cdot {\bf b} +{\bf a}\cdot\frac{d{\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/alpha_x=pislash2-alpha_y=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\alpha_x = \pi/2-\alpha_y=\alpha$">|; 

$key = q/{displaymath}W_2=frac{1}{4pi,epsilon_0}frac{q_2,q_1}{|{{bf{r}_2-{{bf{r}_1|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="\begin{displaymath}
W_2 = \frac{1}{4\pi \epsilon_0} \frac{q_2  q_1}{\vert{\bf r}_2 - {\bf r}_1\vert}.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{B}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$\nabla\cdot {\bf B}=0$">|; 

$key = q/{displaymath}frac{1}{2},m_e,v^2(x)-e,phi(x)=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1480.png"
 ALT="\begin{displaymath}
\frac{1}{2}  m_e v^2(x) - e \phi(x) = 0.
\end{displaymath}">|; 

$key = q/{displaymath}v_g=frac{domega}{dk}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2342.png"
 ALT="\begin{displaymath}
v_g = \frac{d\omega}{dk}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}=N,l,mu_0,N,I,pi,r^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1888.png"
 ALT="\begin{displaymath}
{\mit\Phi} = N l  \mu_0  N I  \pi  r^2.
\end{displaymath}">|; 

$key = q/{displaymath}oint_S{{bf{A}cdotd{{bf{S}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="\begin{displaymath}
\oint_S {\bf A}\cdot d{\bf S} =0
\end{displaymath}">|; 

$key = q/displaystyle-{mitOmega},v_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="$\displaystyle -{\mit\Omega} v_x,$">|; 

$key = q/y=pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1594.png"
 ALT="$y=\pi$">|; 

$key = q/{displaymath}phi(r)=phi_b,ln(rslashb).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2647.png"
 ALT="\begin{displaymath}
\phi(r) = \phi_b \ln(r/b).
\end{displaymath}">|; 

$key = q/displaystylefrac{partial^2T}{partialx^2}+frac{partial^2T}{partialy^2}+frac{partial^2T}{partialz^2}equivnabla^2T.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$\displaystyle \frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial y^2} +
\frac{\partial^2 T}{\partial z^2} \equiv \nabla^2 T.$">|; 

$key = q/displaystylev_perp,cos({mitOmega},t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$\displaystyle v_\perp \cos({\mit\Omega} t),$">|; 

$key = q/{displaymath}nablacdot{{bf{E}=frac{partialE_x}{partialx}+frac{partialE_y}{partia,epsilon_0}frac{3,r^2-3,x^2-3,y^2-3,z^2}{r^5}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="523" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf E} = \frac{\partial E_x}{\partial x}+
\frac...
...pi \epsilon_0} \frac{3 r^2 - 3 x^2-3 y^2-3 z^2}{r^5} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}phi(r,theta)=-E_1,r,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1737.png"
 ALT="\begin{displaymath}
\phi(r,\theta) = - E_1 r \cos\theta.
\end{displaymath}">|; 

$key = q/rslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2986.png"
 ALT="$r/c$">|; 

$key = q/nablatimes{{bf{E}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="$\nabla\times{\bf E} = {\bf0}$">|; 

$key = q/{displaymath}G^{ij}=frac{1}{2},(epsilon^{ijk4}F_{k4}+epsilon^{ij4k}F_{4k})=epsilon^{ijk}F_{k4},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3061.png"
 ALT="\begin{displaymath}
G^{ij} = \frac{1}{2} (\epsilon^{ijk4} F_{k4} + \epsilon^{ij4k}
F_{4k}) = \epsilon^{ijk} F_{k4},
\end{displaymath}">|; 

$key = q/G({{bf{r},,{{bf{r}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="$G({\bf r},  {\bf r}')$">|; 

$key = q/r=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1647.png"
 ALT="$r=a$">|; 

$key = q/displaystyleF_y({{bf{k}cdot{{bf{r}-k,c,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="$\displaystyle F_y ({\bf k}\cdot{\bf r} - k c t),$">|; 

$key = q/{displaymath}frac{dh}{dl}=left(frac{dh}{dl}right)_{{rm{max},costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="\begin{displaymath}
\frac{dh}{dl}= \left(\frac{dh}{dl}\right)_{\rm max}  \cos\theta.
\end{displaymath}">|; 

$key = q/{mitdiv},{{bf{A}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="${\mit div} {\bf A} = 0$">|; 

$key = q/{displaymath}x=r,costheta,~~~y=r,sintheta,~~~z=z,~~~dV=r,dr,dtheta,dz{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="\begin{displaymath}
x = r \cos\theta,&nbsp;&nbsp;&nbsp;y = r \sin\theta,&nbsp;&nbsp;&nbsp;z = z,&nbsp;&nbsp;&nbsp;
dV = r dr d\theta dz
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig18.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig18.eps}}
\end{figure}">|; 

$key = q/{displaymath}partial_muJ^mu=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2967.png"
 ALT="\begin{displaymath}
\partial_\mu J^\mu =0.
\end{displaymath}">|; 

$key = q/d{{bf{S}=(0,,dS_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$d{\bf S} = (0, dS_y, 0)$">|; 

$key = q/l=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="$l=0.1$">|; 

$key = q/t=dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3306.png"
 ALT="$t=dt$">|; 

$key = q/{displaymath}A_z({{bf{r},t)simeqfrac{mu_0,l}{4pi}frac{I(t-rslashc)}{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2219.png"
 ALT="\begin{displaymath}
A_z({\bf r}, t) \simeq \frac{\mu_0  l}{4\pi} \frac{I(t-r/c)}{r}.
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{E}=-frac{partial,nablatimes{{bf{A}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="\begin{displaymath}
\nabla\times{\bf E} = - \frac{\partial  \nabla\times{\bf A}}{\partial t},
\end{displaymath}">|; 

$key = q/displaystyleT^3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2885.png"
 ALT="$\displaystyle T^3,$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right){{bf{A}={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="\begin{displaymath}
\left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}\right) {\bf A} = {\bf0}
\end{displaymath}">|; 

$key = q/nablacdot{{bf{E}_3=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1445.png"
 ALT="$\nabla\cdot {\bf E}_3 = 0$">|; 

$key = q/{displaymath}deltaW=intphi,delta{{bf{D}!cdot!d{{bf{S}-intnablaphi!cdot!delta{{bf{D},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1758.png"
 ALT="\begin{displaymath}
\delta W = \int \phi  \delta{\bf D}\!\cdot\!d{\bf S} -
\int \nabla\phi\!\cdot\!\delta{\bf D} d^3{\bf r},
\end{displaymath}">|; 

$key = q/S_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2954.png"
 ALT="$S_0$">|; 

$key = q/mu>mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1831.png"
 ALT="$\mu&gt;\mu_0$">|; 

$key = q/y'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2700.png"
 ALT="$y'=0$">|; 

$key = q/{{bf{E}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2595.png"
 ALT="${\bf E}_t$">|; 

$key = q/displaystyle|I_0|,exp[{{rm{i},(omega,t-theta)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2024.png"
 ALT="$\displaystyle \vert I_0\vert  \exp[{\rm i} (\omega  t - \theta)].$">|; 

$key = q/displaystyle{{bf{A}(x^i,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3234.png"
 ALT="$\displaystyle {\bf A}(x^i, t)$">|; 

$key = q/partialslashpartialzequiv{{rm{i},k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2574.png"
 ALT="$\partial/\partial z\equiv
{\rm i} k$">|; 

$key = q/A^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3167.png"
 ALT="$A^\mu$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="$p$">|; 

$key = q/dx^2+dy^2+dz^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2681.png"
 ALT="$dx^2 + dy^2 +dz^2$">|; 

$key = q/{displaymath}dW=frac{1}{4pi,epsilon_0}frac{q(r),dq}{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="\begin{displaymath}
dW = \frac{1}{4\pi \epsilon_0} \frac{ q(r) dq}{r}.
\end{displaymath}">|; 

$key = q/{displaymath}{{rm{i},{{bf{k}cdot{{bf{E}_0=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="\begin{displaymath}
{\rm i}  {\bf k} \cdot {\bf E}_0 = 0,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{M}=chi_m,{{bf{H},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1785.png"
 ALT="\begin{displaymath}
{\bf M} = \chi_m  {\bf H},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{m}=frac{1}{2}int{{bf{r}times{{bf{j},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1766.png"
 ALT="\begin{displaymath}
{\bf m} = \frac{1}{2}\int {\bf r}\times{\bf j} d^3{\bf r},
\end{displaymath}">|; 

$key = q/partialslashpartialx^i|_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3240.png"
 ALT="$\partial/\partial x^i\vert _t$">|; 

$key = q/displaystyle(nablatimes{{bf{B})_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$\displaystyle (\nabla\times{\bf B})_x$">|; 

$key = q/{displaymath}{{bf{j}={{bf{j}_t+nablatimes{{bf{M}+frac{partial{{bf{P}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1777.png"
 ALT="\begin{displaymath}
{\bf j} = {\bf j}_t + \nabla\times{\bf M} + \frac{\partial{\bf P}}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{B}_1=nablatimes{{bf{A}_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1870.png"
 ALT="\begin{displaymath}
{\bf B}_1 = \nabla\times {\bf A}_1.
\end{displaymath}">|; 

$key = q/Z_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2098.png"
 ALT="$Z_1$">|; 

$key = q/displaystyle{{bf{B}({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="$\displaystyle {\bf B}({\bf r}, t)$">|; 

$key = q/{displaymath}frac{dE}{dt}={{bf{f}!cdot!{{bf{u}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3169.png"
 ALT="\begin{displaymath}
\frac{d E}{dt} = {\bf f}\!\cdot\!{\bf u}.
\end{displaymath}">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)Grightarr),nabla^2left(frac{1}{|{{bf{r}-{{bf{r}'|}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="\begin{displaymath}
\left(\nabla^2- \frac{1}{c^2}\frac{\partial^2}{\partial t^2}...
..., \nabla^2\left(\frac{1}{\vert{\bf r} - {\bf r}'\vert}\right).
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j}+mu_0epsilon_0,frac{partial{{bf{E}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1778.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0 {\bf j} + \mu_0\epsilon_0 \frac{\partial {\bf E}}
{\partial t},
\end{displaymath}">|; 

$key = q/RneqZ_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2075.png"
 ALT="$R\neq Z_0$">|; 

$key = q/{{bf{M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1767.png"
 ALT="${\bf M}$">|; 

$key = q/displaystylefrac{E_i}{v_1},hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2547.png"
 ALT="$\displaystyle \frac{E_i}{v_1} \hat{\bf y},$">|; 

$key = q/{displaymath}int_{-infty}^{infty}f(x),delta(x),dx,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} f(x) \delta(x) dx,
\end{displaymath}">|; 

$key = q/{displaymath}C_n=frac{2}{pi}int_0^piphi_0(y),sin(n,y),dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1637.png"
 ALT="\begin{displaymath}
C_n = \frac{2}{\pi} \int_0^\pi \phi_0(y) \sin (n y) dy.
\end{displaymath}">|; 

$key = q/dS_4=-d^3x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3292.png"
 ALT="$dS_4=-d^3 x$">|; 

$key = q/displaystyleA_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="$\displaystyle A_y$">|; 

$key = q/displaystylefrac{1}{c^2}frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2572.png"
 ALT="$\displaystyle \frac{1}{c^2}\frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/{{bf{B}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1466.png"
 ALT="${\bf B}_3$">|; 

$key = q/{{bf{B}rightarrow-{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3015.png"
 ALT="${\bf B}\rightarrow -{\bf B}$">|; 

$key = q/{displaymath}U({{bf{r})=frac{1}{4pi}intfrac{D({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="\begin{displaymath}
U({\bf r} ) = \frac{1}{4\pi } \int\frac{D({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'},
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2}intrho,phi,d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \int \rho \phi d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}W=Lint_0^TI,frac{dI}{dt},dt+Rint_0^TI^2,dt,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1949.png"
 ALT="\begin{displaymath}
W = L \int_0^T I \frac{dI}{dt}  dt + R \int_0^T I^2 dt,
\end{displaymath}">|; 

$key = q/displaystyle-G_{4i}=+cB_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3076.png"
 ALT="$\displaystyle - G_{4i} = + cB_i,$">|; 

$key = q/{displaymath}{{bf{e}_pm=frac{1}{2}left(hat{{bf{x}mp{{rm{i},hat{{bf{y}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2367.png"
 ALT="\begin{displaymath}
{\bf e}_\pm = \frac{1}{2}\left(\hat{\bf x} \mp {\rm i} \hat{\bf y}\right).
\end{displaymath}">|; 

$key = q/{{bf{c}=(c_x,,c_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="${\bf c} = (c_x,  c_y,  0)$">|; 

$key = q/displaystylefrac{partialB_y}{partialx}-frac{partialB_x}{partialy}=frac{mu_0I}{2p{r^2}-frac{2,x^2}{r^4}+frac{1}{r^2}-frac{2,y^2}{r^4}right)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="$\displaystyle \frac{\partial B_y}{\partial x} - \frac{\partial B_x}
{\partial y...
...rac{1}{r^2} - \frac{2 x^2}{r^4} +\frac{1}{r^2} -\frac{2  y^2}{r^4}\right) =0,$">|; 

$key = q/{{bf{h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="${\bf h}$">|; 

$key = q/{displaymath}nabla^2{{bf{A}=(nabla^2A_x,,nabla^2A_y,,nabla^2A_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="\begin{displaymath}
\nabla^2{\bf A} = (\nabla^2 A_x,  \nabla^2 A_y,  \nabla^2 A_z).
\end{displaymath}">|; 

$key = q/partialTslashpartialt>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\partial T/\partial t&gt;0$">|; 

$key = q/{displaymath}{{bf{E}=-nablaphi-frac{partial{{bf{A}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="\begin{displaymath}
{\bf E} = -\nabla\phi - \frac{\partial {\bf A}}{\partial t},
\end{displaymath}">|; 

$key = q/{displaymath}sigma_b=-epsilon_0left(left.frac{partialphi}{partialr}right|_{r=a+},epsilon_0,frac{1-epsilon}{1+2,epsilon}costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1752.png"
 ALT="\begin{displaymath}
\sigma_b = -\epsilon_0\left(\left.\frac{\partial\phi}{\parti...
... =
3 \epsilon_0 \frac{1-\epsilon}{1+2 \epsilon}\cos\theta.
\end{displaymath}">|; 

$key = q/displaystyle{mitOmega},v_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$\displaystyle {\mit\Omega} v_y,$">|; 

$key = q/{displaymath}nablacdot{{bf{C}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf C} = 0,
\end{displaymath}">|; 

$key = q/phi_0(y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1595.png"
 ALT="$\phi_0(y)$">|; 

$key = q/{displaymath}g(x,epsilon)=left{array{{lll}1slashepsilon&mbox{hspace{1cm}}&{{rm{f}|x|<epsilonslash20&&{{rm{otherwise}array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="\begin{displaymath}
g(x,\epsilon) = \left\{
\begin{array}{lll}
1/\epsilon &amp;\mbox...
... x\vert &lt; \epsilon/2\\\\
0 &amp;&amp;{\rm otherwise}
\end{array}\right.
\end{displaymath}">|; 

$key = q/{displaymath}phi(0,y)=sum_{n=1}^inftyC_nsin(n,y)=phi_0(y).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1630.png"
 ALT="\begin{displaymath}
\phi(0, y) = \sum_{n=1}^\infty C_n \sin (n y) = \phi_0(y).
\end{displaymath}">|; 

$key = q/displaystylefrac{partialB_z}{partialx}-{{rm{i},k,B_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2586.png"
 ALT="$\displaystyle \frac{\partial B_z}{\partial x}
- {\rm i} k B_x,$">|; 

$key = q/x^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2906.png"
 ALT="$x^\mu$">|; 

$key = q/gammarightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3147.png"
 ALT="$\gamma\rightarrow \infty$">|; 

$key = q/{displaymath}{{bf{B}=frac{{{bf{r}times{{bf{E}}{r,c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3260.png"
 ALT="\begin{displaymath}
{\bf B} = \frac{{\bf r}\times{\bf E}}{r c}.
\end{displaymath}">|; 

$key = q/t=t'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2653.png"
 ALT="$t=t'=0$">|; 

$key = q/{displaymath}F(z)=U(x,y)+{{rm{i},V(x,y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1540.png"
 ALT="\begin{displaymath}
F(z) = U(x, y) + {\rm i} V(x, y),
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}int_{{rm{all,space}E^{2},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1508.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \int_{\rm all space} E^{2} dV.
\end{displaymath}">|; 

$key = q/{{bf{A}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="${\bf A}({\bf r})$">|; 

$key = q/omega(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2337.png"
 ALT="$\omega(k)$">|; 

$key = q/|a|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\vert a\vert$">|; 

$key = q/sqrt{x^2+y^2}leqr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="$\sqrt{x^2+ y^2} \leq r$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$O$">|; 

$key = q/r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="$r^2$">|; 

$key = q/{displaymath}nablatimes{{bf{H}={{bf{j}_t.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1808.png"
 ALT="\begin{displaymath}
\nabla\times{\bf H} = {\bf j}_t.
\end{displaymath}">|; 

$key = q/displaystyle{{rm{RHS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\displaystyle {\rm RHS}$">|; 

$key = q/{{bf{B}_{{rm{rad}=({{bf{r}times{{bf{E}_{{rm{rad})slashr,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3340.png"
 ALT="${\bf B}_{\rm rad} = ({\bf r}\times
{\bf E}_{\rm rad})/r c$">|; 

$key = q/{displaymath}{{bf{B}_0cdot{{bf{k}times{{bf{E}_0=omega,B_0^{~2}>0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="\begin{displaymath}
{\bf B}_0 \cdot {\bf k} \times{\bf E}_0 = \omega B_0^{&nbsp;2} &gt; 0.
\end{displaymath}">|; 

$key = q/E_{x,1}=E_{x,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2554.png"
 ALT="$E_{x 1}=E_{x 2}$">|; 

$key = q/r_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2286.png"
 ALT="$r_e$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig4.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig4.eps}}
\end{figure}">|; 

$key = q/mu,nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2867.png"
 ALT="$\mu, \nu$">|; 

$key = q/a^2=lambda,b^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1530.png"
 ALT="$a^2=\lambda b^2$">|; 

$key = q/(3times10^7)^{-2}sim10^{-15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="$(3\times 10^7)^{-2}
\sim 10^{-15}$">|; 

$key = q/{displaymath}A({{bf{r}',t-|{{bf{r}-{{bf{r}'|slashc)equivleft[A({{bf{r}',t)right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="\begin{displaymath}
A({\bf r}', t- \vert{\bf r} - {\bf r}'\vert/c) \equiv \left[ A({\bf r}', t)\right].
\end{displaymath}">|; 

$key = q/d{mitOmega}=sinalpha,dalpha,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3382.png"
 ALT="$d{\mit\Omega} = \sin\alpha d\alpha d\phi$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="${\bf a}  {\rm x}  {\bf b}= {\bf0}$">|; 

$key = q/{displaymath}dyleft(int_0^{1-y}x^2,y,dxright)=y,dyleft[frac{x^3}{3}right]^{1-y}_0=frac{y}{3},(1-y)^3,dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{displaymath}
dy\left(\int_0^{1-y} x^2  y dx\right) = y dy\left[ \frac{x^3}{3}\right]^{1-y}_0
= \frac{y}{3} (1-y)^3 dy.
\end{displaymath}">|; 

$key = q/displaystyleleft(sintheta_i,,0,,costheta_iright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2517.png"
 ALT="$\displaystyle \left(\sin\theta_i, 0, \cos\theta_i\right),$">|; 

$key = q/z=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$z= r \cos\theta$">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{E}+q,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="\begin{displaymath}
{\bf f} = q {\bf E} + q {\bf v} \times{\bf B}.
\end{displaymath}">|; 

$key = q/{displaymath}C=frac{Q}{V}=4pi,epsilon_0,a.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="\begin{displaymath}
C = \frac{Q}{V} = 4\pi  \epsilon_0  a.
\end{displaymath}">|; 

$key = q/F(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1535.png"
 ALT="$F(z)$">|; 

$key = q/{displaymath}frac{d{{bf{r}}{dt'}=-{{bf{u}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3232.png"
 ALT="\begin{displaymath}
\frac{d{\bf r}}{dt'}= -{\bf u}.
\end{displaymath}">|; 

$key = q/{{bf{B}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2504.png"
 ALT="${\bf B}_t$">|; 

$key = q/displaystyleleft(frac{alpha-beta}{alpha+beta}right)E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2559.png"
 ALT="$\displaystyle \left(\frac{\alpha-\beta}{\alpha+\beta}\right) E_i,$">|; 

$key = q/{displaymath}v_g=c,sqrt{1-frac{omega_p^{,2}}{omega^2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2345.png"
 ALT="\begin{displaymath}
v_g = c \sqrt{1-\frac{\omega_p^{ 2}}{\omega^2}},
\end{displaymath}">|; 

$key = q/x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$x_1$">|; 

$key = q/displaystylefrac{dy'}{dt'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2739.png"
 ALT="$\displaystyle \frac{dy'}{dt'},$">|; 

$key = q/{displaymath}sigma_b=epsilon_0,,frac{partialphi(z=0-)}{partialz}-epsilon_0,,fracsilon_2+epsilon_1)}frac{d}{(r^2+d^2)^{3slash2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1726.png"
 ALT="\begin{displaymath}
\sigma_b = \epsilon_0  \frac{\partial\phi(z=0-)}{\partial ...
...{\epsilon_1(\epsilon_2+\epsilon_1)} \frac{d}{(r^2+d^2)^{3/2}}.
\end{displaymath}">|; 

$key = q/displaystylefrac{partialU}{partialx}+{{rm{i},frac{partialV}{partialx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1553.png"
 ALT="$\displaystyle \frac{\partial U}{\partial x} + {\rm i}  \frac{\partial V}
{\partial x}.$">|; 

$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="$\psi$">|; 

$key = q/{displaymath}A_z(y+dy),dz-A_z(y),dz=frac{partialA_z}{partialy},dy,dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="\begin{displaymath}
A_z(y+dy) dz - A_z(y) dz = \frac{\partial A_z}{\partial y}  dy dz.
\end{displaymath}">|; 

$key = q/displaystyleW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1959.png"
 ALT="$\displaystyle W$">|; 

$key = q/{displaymath}I=intT^4,d^3x,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3285.png"
 ALT="\begin{displaymath}
I = \int T^4 d^3 x,
\end{displaymath}">|; 

$key = q/{displaymath}T=frac{I_t}{I_i}=frac{v_1}{v_2}left(frac{E_t}{E_i}right)^2=frac{n_2}{n_1}left(frac{E_t}{E_i}right)^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2484.png"
 ALT="\begin{displaymath}
T = \frac{I_t}{I_i} =\frac{v_1}{v_2}\left(\frac{E_t}{E_i}\right)^2=\frac{n_2}{n_1}\left(\frac{E_t}{E_i}\right)^2.
\end{displaymath}">|; 

$key = q/displaystylefrac{u_1-v}{1-u_1,vslashc^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2747.png"
 ALT="$\displaystyle \frac{u_1-v}{1-u_1  v/c^2},$">|; 

$key = q/displaystylefrac{E_t}{v_2},left(-costheta_t,,0,,sintheta_tright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2533.png"
 ALT="$\displaystyle \frac{E_t}{v_2} \left(-\cos\theta_t, 0, \sin\theta_t\right),$">|; 

$key = q/displaystylephi_S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1404.png"
 ALT="$\displaystyle \phi_S,$">|; 

$key = q/d{{bf{l}=(dx,,dy);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="$d{\bf l}=(dx, dy)$">|; 

$key = q/displaystylemu_0,{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$\displaystyle \mu_0  {\bf j}$">|; 

$key = q/I_1,I_2<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1968.png"
 ALT="$I_1  I_2 &lt;0$">|; 

$key = q/intrho({{bf{r}'),d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$\int \rho({\bf r}') d^3{\bf r}'$">|; 

$key = q/I_1,R_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1921.png"
 ALT="$I_1  R_1$">|; 

$key = q/dx^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2800.png"
 ALT="$dx^i$">|; 

$key = q/displaystyleoint_C{{bf{E}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="$\displaystyle \oint_C {\bf E} \cdot d{\bf l}$">|; 

$key = q/E_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2372.png"
 ALT="$E_-$">|; 

$key = q/displaystyle~_{lim|deltay|rightarrow0}frac{U(x,y+deltay)+{{rm{i},V(x,y+deltay)-U(x,y)-{{rm{i},V(x,y)}{{{rm{i},deltay};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1555.png"
 ALT="$\displaystyle&nbsp;_{\lim \vert\delta y\vert\rightarrow 0}
\frac{U(x, y+\delta y) + {\rm i}  V(x, y+\delta y) - U(x, y) - {\rm i} 
V(x,y)}{{\rm i} \delta y}$">|; 

$key = q/displaystyle{{bf{I}times({{bf{r}-{{bf{r}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$\displaystyle {\bf I} \times({\bf r} - {\bf r}')$">|; 

$key = q/{displaymath}sigma_b=epsilon_0,(E_{perp,2}-E_{perp,1}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1694.png"
 ALT="\begin{displaymath}
\sigma_b = \epsilon_0 (E_{\perp 2}-E_{\perp 1}).
\end{displaymath}">|; 

$key = q/displaystyleG^{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3064.png"
 ALT="$\displaystyle G^{i4}$">|; 

$key = q/{{rm{TE}_{00};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2620.png"
 ALT="${\rm TE}_{00}$">|; 

$key = q/displaystylex^2-y^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1544.png"
 ALT="$\displaystyle x^2 - y^2,$">|; 

$key = q/A_{ijkl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2773.png"
 ALT="$A_{ijkl}$">|; 

$key = q/d{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$d{\bf l}$">|; 

$key = q/{displaymath}frac{E_theta,B_phi}{mu_0}=frac{e^2}{16pi^2,epsilon_0,c^3}frac{sin^2theta}{r^2},dot{u}^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3282.png"
 ALT="\begin{displaymath}
\frac{E_\theta  B_\phi}{\mu_0} = \frac{e^2}
{16\pi^2  \epsilon_0  c^3}\frac{\sin^2\theta}{r^2}  \dot{u}^2.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="$\displaystyle {\bf E}$">|; 

$key = q/{displaymath}V=frac{q}{C}=left.int_0^tI,dtrightslashC,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2004.png"
 ALT="\begin{displaymath}
V = \frac{q}{C} = \left.\int_0^t I dt\right/C,
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}_i=int{{bf{B}cdotd{{bf{S}_i=oint{{bf{A}cdotd{{bf{l}_i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1976.png"
 ALT="\begin{displaymath}
{\mit\Phi}_i = \int {\bf B} \cdot d{\bf S}_i = \oint {\bf A} \cdot d{\bf l}_i,
\end{displaymath}">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\delta$">|; 

$key = q/rho({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$\rho({\bf r})$">|; 

$key = q/k_r,d=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2409.png"
 ALT="$k_r d= 1$">|; 

$key = q/{displaymath}V=frac{q}{2pi,epsilon_0}lnfrac{b}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1393.png"
 ALT="\begin{displaymath}
V = \frac{q}{2\pi  \epsilon_0} \ln \frac{b}{a}.
\end{displaymath}">|; 

$key = q/{displaymath}C=frac{2pi,epsilon_0}{ln(bslasha)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2066.png"
 ALT="\begin{displaymath}
C = \frac{ 2\pi  \epsilon_0}{\ln (b/a)}.
\end{displaymath}">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2} \right) G = 0,
\end{displaymath}">|; 

$key = q/displaystyleY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1618.png"
 ALT="$\displaystyle Y$">|; 

$key = q/dt>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2666.png"
 ALT="$dt&gt;0$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{[{{bf{j}({{bf{r}')]}{|{{bf{r}-{{bf{r}'|},dV'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2983.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int
\frac{[{\bf j}({\bf r}')]}{\vert{\bf r}- {\bf r}'\vert} dV'.$">|; 

$key = q/{displaymath}oint_S{{bf{j}cdotd{{bf{S}=-frac{partial}{partialt}!int_Vrho,dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="\begin{displaymath}
\oint_S {\bf j} \cdot d{\bf S} = - \frac{\partial}{\partial t}\!
\int_V \rho dV.
\end{displaymath}">|; 

$key = q/pmcalV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1576.png"
 ALT="$\pm \cal V$">|; 

$key = q/displaystyle|V_0|,|I_0|int_{omegat=0}^{omegat=2pi}cos(omega,t),cos(omega,t-theta),,frac{d(omega,t)}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2018.png"
 ALT="$\displaystyle \vert V_0\vert  \vert I_0\vert \int_{\omega t = 0}^{\omega t = 2\pi}
\cos(\omega  t)  \cos(\omega  t - \theta)  \frac{d(\omega  t)}{2\pi}$">|; 

$key = q/omegallomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2307.png"
 ALT="$\omega \ll
\omega_0$">|; 

$key = q/{displaymath}{{bf{curl},{{bf{A}=left(frac{partialA_z}{partialy}-frac{partialA_y}A_y}{partialx}-frac{partialA_x}{partialy}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="\begin{displaymath}
{\bf curl} {\bf A} = \left(\frac{\partial A_z}{\partial y}-...
...ial A_y}{\partial x}- \frac{\partial A_x}
{\partial y}\right).
\end{displaymath}">|; 

$key = q/{displaymath}int_V(nablaphi_3)^2,dV=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1415.png"
 ALT="\begin{displaymath}
\int_V (\nabla \phi_3)^2 dV = 0.
\end{displaymath}">|; 

$key = q/B_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1835.png"
 ALT="$B_g$">|; 

$key = q/{{bf{e}_xtimes{{bf{e}_y={{bf{e}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="${\bf e}_x\times
{\bf e}_y={\bf e}_z$">|; 

$key = q/{displaymath}P_{{rm{heat}=langleI^2Rrangle=frac{1}{2}I_0^{,2}R,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2233.png"
 ALT="\begin{displaymath}
P_{\rm heat} = \langle I^2 R\rangle = \frac{1}{2} I_0^{ 2} R,
\end{displaymath}">|; 

$key = q/S,cosalpha_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$S \cos\alpha_x$">|; 

$key = q/{displaymath}B_{perp,2}-B_{perp,1}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1809.png"
 ALT="\begin{displaymath}
B_{\perp 2}-B_{\perp 1}= 0,
\end{displaymath}">|; 

$key = q/{mitDelta}omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3399.png"
 ALT="${\mit\Delta} \omega$">|; 

$key = q/1300;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2162.png"
 ALT="$1300$">|; 

$key = q/{displaymath}E_perp=frac{sigma}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="\begin{displaymath}
E_\perp = \frac{\sigma}{\epsilon_0}
\end{displaymath}">|; 

$key = q/{displaymath}V_1=R_1,I_1+L_1frac{dI_1}{dt}+M,frac{dI_2}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1925.png"
 ALT="\begin{displaymath}
V_1 = R_1  I_1 + L_1 \frac{dI_1}{dt} + M \frac{dI_2}{dt}.
\end{displaymath}">|; 

$key = q/B_j^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2776.png"
 ALT="$B_j^i$">|; 

$key = q/{displaymath}{calF}_mu=gammaleft(-{{bf{f},frac{{{bf{f}!cdot!{{bf{u}}{c}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3176.png"
 ALT="\begin{displaymath}
{\cal F}_\mu = \gamma\left(-{\bf f}, \frac{{\bf f}\!\cdot\!{\bf u}}{c}
\right),
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2522.png"
 ALT="$\displaystyle {\bf E}_i$">|; 

$key = q/B_{ik};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3016.png"
 ALT="$B_{ik}$">|; 

$key = q/h(x,,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$h(x, y)$">|; 

$key = q/{displaymath}A_i=g_{ij},A^j.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2837.png"
 ALT="\begin{displaymath}
A_i = g_{ij}  A^j.
\end{displaymath}">|; 

$key = q/displaystyleE_{{rm{upper};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$\displaystyle E_{\rm upper }$">|; 

$key = q/{displaymath}W=frac{1}{2}sum_{i=1}^Nq_i,phi_i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \sum_{i=1}^N q_i  \phi_i,
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2G({{bf{r},{{bf{r}')=delta({{bf{r}-{{bf{r}').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="\begin{displaymath}
\nabla^2 G({\bf r}, {\bf r}') = \delta({\bf r} - {\bf r}').
\end{displaymath}">|; 

$key = q/{{bf{B}=mu_0,{{bf{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2466.png"
 ALT="${\bf B}=\mu_0 
{\bf H}$">|; 

$key = q/{displaymath}epsilon^{alphabetagammadelta},p_{alpha}^{alpha'},p_{beta}^{beta'},p,|p_mu^{mu'}|=epsilon^{alpha'beta'gamma'delta'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img3000.png"
 ALT="\begin{displaymath}
\epsilon^{\alpha\beta\gamma\delta}
 p_{\alpha}^{\alpha'} p...
...t p_\mu^{\mu'}\vert = \epsilon^{\alpha'
\beta'\gamma'\delta'},
\end{displaymath}">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$T$">|; 

$key = q/displaystyleW_y({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$\displaystyle W_y({\bf r} )$">|; 

$key = q/displaystylefrac{1}{2}left(epsilon_0,E^2+frac{B^2}{mu_0}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3211.png"
 ALT="$\displaystyle \frac{1}{2} \left(\epsilon_0  E^2 +\frac{B^2}{\mu_0}\right).$">|; 

$key = q/{displaymath}x^1=x,~~x^2=y,~~x^3=z,~~x^4=c,t,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2861.png"
 ALT="\begin{displaymath}
x^1=x,&nbsp;&nbsp;x^2=y,&nbsp;&nbsp;x^3= z,&nbsp;&nbsp;x^4=c t,
\end{displaymath}">|; 

$key = q/{displaymath}V=eta,frac{l}{A},I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="\begin{displaymath}
V = \eta  \frac{l}{A}  I.
\end{displaymath}">|; 

$key = q/displaystyle(a_y,b_z-a_z,b_y)^2+(a_z,b_x-a_x,b_z)^2+(a_x,b_z-a_y,b_x)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle (a_y  b_z-a_z  b_y)^2 +(a_z  b_x - a_x  b_z)^2 +(a_x  b_z
-a_y  b_x)^2$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig34.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig34.eps}}
\end{figure}">|; 

$key = q/{{bf{v}=d{{bf{r}slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2354.png"
 ALT="${\bf v} = d{\bf r}/dt$">|; 

$key = q/I=intT^4,d^3x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3294.png"
 ALT="$I = \int T^4 d^3 x$">|; 

$key = q/{displaymath}-A_muA^mu=gamma^2left(frac{dgamma}{dt},{{bf{u}+gamma,dot{{bf{u}right)^2-gamma^2,c^2left(frac{dgamma}{dt}right)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img3318.png"
 ALT="\begin{displaymath}
-A_\mu A^\mu = \gamma^2\left(\frac{d\gamma}{dt} {\bf u} + \...
...u}\right)^2 - \gamma^2  c^2\left(\frac{d\gamma}{dt}\right)^2,
\end{displaymath}">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="$\sigma$">|; 

$key = q/{displaymath}omega_p=sqrt{frac{n_e,e^2}{epsilon_0,m_e}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2326.png"
 ALT="\begin{displaymath}
\omega_p = \sqrt{\frac{n_e e^2}{\epsilon_0 m_e}}
\end{displaymath}">|; 

$key = q/g_{ij},dx^i,dx^j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2843.png"
 ALT="$g_{ij} dx^i  dx^j$">|; 

$key = q/displaystylea_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle a_{y'}$">|; 

$key = q/F_{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3039.png"
 ALT="$F_{\mu\nu}$">|; 

$key = q/z=lslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2206.png"
 ALT="$z=l/2$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="${\bf a}  {\rm x}  {\bf b}$">|; 

$key = q/{displaymath}{{bf{E}_3={{bf{E}_1-{{bf{E}_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1438.png"
 ALT="\begin{displaymath}
{\bf E}_3 = {\bf E}_1 - {\bf E}_2.
\end{displaymath}">|; 

$key = q/F^{44}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3050.png"
 ALT="$F^{44}= 0$">|; 

$key = q/A=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$A=+1$">|; 

$key = q/displaystylefrac{rho}{cosphi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="$\displaystyle \frac{\rho}{\cos\phi} .$">|; 

$key = q/{{bf{E}rightarrowE_0,hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1646.png"
 ALT="${\bf E}\rightarrow E_0 \hat{\bf z}$">|; 

$key = q/displaystylec_x,costheta+c_y,sintheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle c_x \cos\theta
+c_y \sin\theta.$">|; 

$key = q/I';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="$I'$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$\eta$">|; 

$key = q/displaystyle+k,dz,dt+l,dy,dz+m,dx,dz+n,dx,dy,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2673.png"
 ALT="$\displaystyle + k  dz  dt + l  dy  dz + m  dx  dz
+ n  dx  dy,$">|; 

$key = q/v=1slashsqrt{L,C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2055.png"
 ALT="$v= 1/\sqrt{L C}$">|; 

$key = q/{displaymath}B_i=frac{1}{2},epsilon_{ijk}B^{jk}=-frac{mu_0,e}{4pi,{r'}^3},gamma(u),epsilon_{ijk},u^j,r^k,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3135.png"
 ALT="\begin{displaymath}
B_i = \frac{1}{2}  \epsilon_{ijk} B^{jk} = -\frac{\mu_0 e}{4\pi {r'}^3}
 \gamma(u) \epsilon_{ijk}  u^j  r^k,
\end{displaymath}">|; 

$key = q/v_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$v_\perp$">|; 

$key = q/{{bf{j}({{bf{r})=q,n,{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="${\bf j}({\bf r})
= q  n  {\bf v}$">|; 

$key = q/omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2299.png"
 ALT="$\omega_0$">|; 

$key = q/{mitDelta}varphi(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2394.png"
 ALT="${\mit\Delta}\varphi(\omega)$">|; 

$key = q/{{bf{E}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1425.png"
 ALT="${\bf E}_2$">|; 

$key = q/B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1813.png"
 ALT="$B_0$">|; 

$key = q/{displaymath}B=mu_0,N,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1972.png"
 ALT="\begin{displaymath}
B = \mu_0  N I,
\end{displaymath}">|; 

$key = q/D(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$D(x,y)$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}times{{bf{c}=-{{bf{a}cdot{{bf{c}times{{bf{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b}\times{\bf c} = - {\bf a} \cdot {\bf c}\times{\bf b}.
\end{displaymath}">|; 

$key = q/F^{ij}=-c,B^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3132.png"
 ALT="$F^{ij} = - c B^{ij}$">|; 

$key = q/{displaymath}frac{partialU}{partialt}+nablacdot{{bf{u}=-{{bf{E}cdot{{bf{j}_t,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2132.png"
 ALT="\begin{displaymath}
\frac{\partial U}{\partial t} + \nabla\cdot{\bf u} = -{\bf E}\cdot {\bf j}_t,
\end{displaymath}">|; 

$key = q/displaystylev_parallel,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$\displaystyle v_\parallel t.$">|; 

$key = q/displaystyle{{bf{B}(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2451.png"
 ALT="$\displaystyle {\bf B}(z,t)$">|; 

$key = q/10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="$10^{-6}$">|; 

$key = q/chi_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1786.png"
 ALT="$\chi_m$">|; 

$key = q/langle,rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2148.png"
 ALT="$\langle  \rangle$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}')}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1395.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \frac{1}{4\pi  \epsilon_0} \int \frac{\rho({\bf r}')}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/c-v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2659.png"
 ALT="$c-v$">|; 

$key = q/{displaymath}F^{jk}=-c,B^{jk}=frac{e}{4pi,epsilon_0,c,{r'}^3},gamma(u),(u^j,r^k-u^k,r^j),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img3134.png"
 ALT="\begin{displaymath}
F^{jk} = -c B^{jk}=
\frac{e}{4\pi \epsilon_0 c {r'}^3} \gamma(u) (u^j  r^k-u^k  r^j),
\end{displaymath}">|; 

$key = q/{{bf{E}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1424.png"
 ALT="${\bf E}_1$">|; 

$key = q/{{bf{B}_0rightarrow{{bf{B}_0,{{rm{e}^{,{{rm{i},phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="${\bf B}_0 \rightarrow {\bf B}_0  {\rm e}^{ {\rm i} \phi}$">|; 

$key = q/oplus;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="$\oplus$">|; 

$key = q/{displaymath}-frac{partial}{partialt}!int_VU,dV=oint_S{{bf{u}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2109.png"
 ALT="\begin{displaymath}
-\frac{\partial}{\partial t}\!\int_V U d V = \oint_S {\bf u}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/arightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="$a\rightarrow 0$">|; 

$key = q/delta_{ij}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2192.png"
 ALT="$\delta_{ij}=1$">|; 

$key = q/lambda>20,000,{{rm{km};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2423.png"
 ALT="$\lambda &gt; 20,000 {\rm km}$">|; 

$key = q/{displaymath}{{bf{E}+frac{partial{{bf{A}}{partialt}=-nablaphi,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="\begin{displaymath}
{\bf E} + \frac{\partial {\bf A} }{\partial t} = -\nabla\phi,
\end{displaymath}">|; 

$key = q/d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="$d^3{\bf r}'$">|; 

$key = q/{displaymath}V=-frac{d{mitPhi}}{dt}=-L,frac{dI}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1891.png"
 ALT="\begin{displaymath}
V = - \frac{d {\mit\Phi}}{d t} = - L  \frac{d I}{dt},
\end{displaymath}">|; 

$key = q/dPslashd{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2269.png"
 ALT="$dP/d{\mit\Omega}$">|; 

$key = q/displaystyle+frac{sigma}{epsilon_0}mbox{hspace{1.85cm}above},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="$\displaystyle +\frac{\sigma }{\epsilon_0} \mbox{\hspace{1.85cm} above},$">|; 

$key = q/displaystylec,A_3'=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3114.png"
 ALT="$\displaystyle c A_3' = 0,$">|; 

$key = q/displaystylefrac{E_t}{v_2},{{rm{e}^{,{{rm{i},(k_2,z-omega,t)},hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2458.png"
 ALT="$\displaystyle \frac{E_t}{v_2} {\rm e}^{ {\rm i} (k_2 z-\omega t)} \hat{\bf y},$">|; 

$key = q/{displaymath}int!int_Sx^2,y,dx,dy,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="\begin{displaymath}
\int\!\int_S x^2  y dx dy,
\end{displaymath}">|; 

$key = q/{{bf{curl},{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="${\bf curl} {\bf A}$">|; 

$key = q/displaystyle|I_0|,cos(omega,t-theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2016.png"
 ALT="$\displaystyle \vert I_0\vert  \cos(\omega  t - \theta),$">|; 

$key = q/{displaymath}q(t)=q_0sin,(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2200.png"
 ALT="\begin{displaymath}
q(t) = q_0 \sin  (\omega  t).
\end{displaymath}">|; 

$key = q/{displaymath}deltaW=intphi,nabla!cdot!delta{{bf{D},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1755.png"
 ALT="\begin{displaymath}
\delta W = \int \phi \nabla\!\cdot\!\delta {\bf D} d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}int_0^1dxint_0^1x^2,y,dy=left(int_0^1x^2,dxright)left(int_0^1y,dyright)=frac{1}{3},frac{1}{2}=frac{1}{6},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="\begin{displaymath}
\int_0^1 dx \int_0^1 x^2  y dy = \left(\int_0^1 x^2 dx\ri...
...nt_0^1 y  dy\right) = \frac{1}{3} \frac{1}{2} = \frac{1}{6},
\end{displaymath}">|; 

$key = q/1000^circ,{{rm{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2296.png"
 ALT="$1000^\circ {\rm C}$">|; 

$key = q/pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2036.png"
 ALT="$\pi/2$">|; 

$key = q/x=0,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2607.png"
 ALT="$x=0, a$">|; 

$key = q/nablacdot{{bf{j}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="$\nabla\cdot{\bf j} \neq 0$">|; 

$key = q/{displaymath}W=sum_{i=1}^Nint_0^TI_i,frac{d{mitPhi}_i}{dt},dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1983.png"
 ALT="\begin{displaymath}
W = \sum_{i=1}^N \int_0^T I_i  \frac{d{\mit\Phi}_i}{dt} dt.
\end{displaymath}">|; 

$key = q/N_2slashN_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1941.png"
 ALT="$N_2/N_1$">|; 

$key = q/G_{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3080.png"
 ALT="$G_{\mu\nu}$">|; 

$key = q/{displaymath}nablacdot{{bf{A}=frac{1}{r^2}frac{partial}{partialr}(r^2,A_r)+frac{rac{1}{r,sintheta}frac{partialA_phi}{partialphi}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="459" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf A} = \frac{1}{r^2}\frac{\partial}{\partial r...
...)
+\frac{1}{r \sin\theta}\frac{\partial A_\phi}{\partial\phi}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{j}={{bf{E}={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="\begin{displaymath}
{\bf j} = {\bf E} = {\bf0}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}({{bf{r})=sum_{i=1}^Nfrac{q_i}{4pi,epsilon_0}frac{{{bf{r}-{{bf{r}_i}{|{{bf{r}-{{bf{r}_i|^3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="\begin{displaymath}
{\bf E}({\bf r}) = \sum_{i=1}^N \frac{q_i}{4\pi \epsilon_0}
\frac{{\bf r}- {\bf r}_i}{\vert{\bf r}-{\bf r}_i\vert^3}.
\end{displaymath}">|; 

$key = q/{displaymath}U_B=frac{B^2}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2105.png"
 ALT="\begin{displaymath}
U_B = \frac{B^2}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}phi_i=frac{partialphi}{partialx^i},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2803.png"
 ALT="\begin{displaymath}
\phi_i = \frac{\partial\phi}{\partial x^i},
\end{displaymath}">|; 

$key = q/{x^i}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3225.png"
 ALT="${x^i}'$">|; 

$key = q/{displaymath}int_{-infty}^{infty}f(x),delta(x-x_0),dx=f(x_0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} f(x) \delta(x-x_0) dx = f(x_0).
\end{displaymath}">|; 

$key = q/a_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$a_z$">|; 

$key = q/(1slashsqrt{2},1slashsqrt{2},0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2680.png"
 ALT="$(1/\sqrt{2}, 1/\sqrt{2}, 0, 1)$">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=lim_{deltatrightarrow0}left[frac{{{bf{a}(t+deltat)-{{bf{a}(t)}{deltat}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \lim_{\delta t\rightarrow 0} \left[\frac{{\bf a}(t+\delta t) - {\bf a}(t)}
{\delta t}\right].
\end{displaymath}">|; 

$key = q/displaystylex',costheta-y',sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$\displaystyle x'  \cos\theta - y' \sin\theta,$">|; 

$key = q/A=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="$A=0.01$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig49.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img2490.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig49.eps}}
\end{figure}">|; 

$key = q/displaystylefrac{J^nu}{c,epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3090.png"
 ALT="$\displaystyle \frac{J^\nu}{c \epsilon_0},$">|; 

$key = q/{displaymath}{{bf{E}cdot{{bf{B}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="\begin{displaymath}
{\bf E} \cdot {\bf B} = 0.
\end{displaymath}">|; 

$key = q/{{bf{b}times{{bf{c}=(0,,0,,b_x,c_y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="${\bf b}\times{\bf c} = (0, 0, b_x  c_y)$">|; 

$key = q/{displaymath}mbox{{boldmath{{omega{}=lim_{deltatrightarrow0}frac{deltambox{{boldmath{{theta{}}{deltat},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="\begin{displaymath}
\mbox{\boldmath$\omega$} = \lim_{\delta t\rightarrow 0} \frac{\delta
\mbox{\boldmath$\theta$} }{\delta t},
\end{displaymath}">|; 

$key = q/a_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3149.png"
 ALT="$a_0$">|; 

$key = q/{displaymath}lambda=frac{2pi}{k}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="\begin{displaymath}
\lambda = \frac{2\pi}{k}
\end{displaymath}">|; 

$key = q/t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="$t_0$">|; 

$key = q/{displaymath}{{bf{B}=nablatimes{{bf{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="\begin{displaymath}
{\bf B} = \nabla\times{\bf A}.
\end{displaymath}">|; 

$key = q/1.6022times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="$1.6022\times 10^{-19}$">|; 

$key = q/{displaymath}g_{mu'nu'},p_{musigma}^{mu'},p_{nu}^{nu'}+g_{mu'nu'},p_{sigma}^{mu'},p_{numu}^{nu'}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2921.png"
 ALT="\begin{displaymath}
g_{\mu'\nu'} p_{\mu\sigma}^{\mu'}  
p_{\nu}^{\nu'} + g_{\mu'\nu'} p_{\sigma}^{\mu'} 
p_{\nu\mu}^{\nu'} = 0.
\end{displaymath}">|; 

$key = q/I_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="$I_i$">|; 

$key = q/{displaymath}({{bf{a}times{{bf{b})^i=epsilon^{ijk},a_j,b_k,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3004.png"
 ALT="\begin{displaymath}
({\bf a}\times{\bf b})^i = \epsilon^{ijk} a_j  b_k,
\end{displaymath}">|; 

$key = q/{displaymath}T=frac{costheta_t}{costheta_i},frac{v_1}{v_2}left(frac{E_t}{E_i}rig^2=alpha,betaleft(frac{2}{1+alpha,beta}right)^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2545.png"
 ALT="\begin{displaymath}
T = \frac{\cos\theta_t}{\cos\theta_i} \frac{v_1}{v_2}\left(...
...t)^2 = \alpha \beta \left(\frac{2}{1+\alpha \beta}\right)^2.
\end{displaymath}">|; 

$key = q/partial^2slashpartialt^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="$\partial^2/\partial t^2$">|; 

$key = q/{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="${\bf a}\times{\bf b}$">|; 

$key = q/displaystyleE_{parallel,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2461.png"
 ALT="$\displaystyle E_{\parallel 1}$">|; 

$key = q/{displaymath}{{bf{F}=q,nA,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="\begin{displaymath}
{\bf F} = q n A  {\bf v}\times{\bf B}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}={{bf{E}_0,{{rm{e}^{,{{rm{i},(k,z-omega,t)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2398.png"
 ALT="\begin{displaymath}
{\bf E} = {\bf E}_0 {\rm e}^{ {\rm i} (k z-\omega t)},
\end{displaymath}">|; 

$key = q/{displaymath}phi_{{rm{analogue}(z=0)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1490.png"
 ALT="\begin{displaymath}
\phi_{\rm analogue}(z=0) = 0,
\end{displaymath}">|; 

$key = q/displaystylefrac{dy}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2732.png"
 ALT="$\displaystyle \frac{dy}{dt},$">|; 

$key = q/{displaymath}{{bf{grad},(phi,psi)=phi,,{{bf{grad},psi+psi,,{{bf{grad},phi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="286" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="\begin{displaymath}
{\bf grad} (\phi  \psi) = \phi   {\bf grad} \psi +\psi   {\bf grad} \phi
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_{{rm{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3276.png"
 ALT="$\displaystyle {\bf B}_{\rm rad}$">|; 

$key = q/displaystyle-frac{e}{4pi,epsilon_0}frac{{{bf{r}'}{{r'}^3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3127.png"
 ALT="$\displaystyle -\frac{e}{4\pi \epsilon_0} \frac{{\bf r}'}{{r'}^3}.$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G=delta({{bf{r}-{{bf{r}'),delta(t-t').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right)G=
\delta({\bf r} - {\bf r}')  \delta(t-t').
\end{displaymath}">|; 

$key = q/{displaymath}v=frac{1}{sqrt{L,C}}=frac{c}{sqrt{epsilon}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2072.png"
 ALT="\begin{displaymath}
v = \frac{1}{\sqrt{L C}}= \frac{c}{\sqrt{\epsilon}}.
\end{displaymath}">|; 

$key = q/{displaymath}epsilon_1,(E_i-E_r),sintheta_i=epsilon_2,E_i,sintheta_t.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2557.png"
 ALT="\begin{displaymath}
\epsilon_1 (E_i-E_r) \sin\theta_i = \epsilon_2 E_i \sin\theta_t.
\end{displaymath}">|; 

$key = q/RggR_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="$R\gg R_0$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{rho({{bf{r}',t')}{4pi,epsilon_0}frac{1}{2}left(r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|}right),?{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="540" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{\rho({\bf r}' ,t ')} {4\pi  \epsil...
...r} - {\bf r}'\vert/c)}{\vert{\bf r} - {\bf r}'\vert}\right) ?
\end{displaymath}">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \frac{{\bf j}({\bf r}')}
{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r}'.$">|; 

$key = q/displaystylenablatimes{{bf{F}={{bf{C},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="$\displaystyle \nabla\times{\bf F} = {\bf C},$">|; 

$key = q/{{bf{a}cdot{{bf{b}times{{bf{c}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$ {\bf a}\cdot{\bf b} \times{\bf c} \neq 0$">|; 

$key = q/{{bf{r'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="${\bf r'}$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$a$">|; 

$key = q/k_r,dgg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2405.png"
 ALT="$k_r d\gg 1$">|; 

$key = q/displaystyleE_xpm{{rm{i},E_y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2361.png"
 ALT="$\displaystyle E_x\pm {\rm i} E_y.$">|; 

$key = q/-q(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2199.png"
 ALT="$-q(t)$">|; 

$key = q/F(P);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$F(P)$">|; 

$key = q/cslashsqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2323.png"
 ALT="$c/\sqrt{\epsilon}$">|; 

$key = q/{displaymath}nabla^2f=frac{1}{r}frac{partial}{partialr}!left(r,frac{partialf}{pa2f}{partialtheta^2}+frac{partial^2f}{partialz^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="\begin{displaymath}
\nabla^2 f = \frac{1}{r}\frac{\partial }{\partial r}\!\left(...
...tial^2 f}{\partial\theta^2}+
\frac{\partial^2 f}{\partial z^2}
\end{displaymath}">|; 

$key = q/{displaymath}epsilon_1,nabla!cdot!{{bf{E}=frac{rho}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1696.png"
 ALT="\begin{displaymath}
\epsilon_1  \nabla\!\cdot\!{\bf E} = \frac{\rho}{\epsilon_0}
\end{displaymath}">|; 

$key = q/displaystyle{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$\displaystyle {\bf A}$">|; 

$key = q/displaystylefrac{n_2}{n_1}left(frac{2,n_1}{n_1+n_2}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2488.png"
 ALT="$\displaystyle \frac{n_2}{n_1}\left(\frac{2 n_1}{n_1+n_2}\right)^2.$">|; 

$key = q/displaystyleE_r,(costheta_i,,0,,sintheta_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2548.png"
 ALT="$\displaystyle E_r (\cos\theta_i,  0, \sin\theta_i),$">|; 

$key = q/muneqnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2872.png"
 ALT="$\mu\neq \nu$">|; 

$key = q/displaystyle-frac{E_r}{v_1},{{rm{e}^{,{{rm{i},(-k_1,z-omega,t)},hat{{bf{y}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2456.png"
 ALT="$\displaystyle -\frac{E_r}{v_1} {\rm e}^{ {\rm i} (-k_1 z-\omega t)} \hat{\bf y}.$">|; 

$key = q/dx=dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$dx=dy$">|; 

$key = q/{displaymath}int_V{nabla}cdot{{bf{E},,d^3{{bf{r}=frac{q}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="\begin{displaymath}
\int_V {\nabla}\cdot{\bf E}  d^3{\bf r} = \frac{q}{\epsilon_0}
\end{displaymath}">|; 

$key = q/RslashR_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="$R/R_0$">|; 

$key = q/n=gamma(u),n_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2956.png"
 ALT="$n=\gamma(u)  n_0$">|; 

$key = q/displaystyleoint_S{{bf{E}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$\displaystyle \oint_S {\bf E} \cdot d{\bf S}$">|; 

$key = q/displaystyleu_2';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2738.png"
 ALT="$\displaystyle u_2'$">|; 

$key = q/{displaymath}omega^2=k^2,c^2+omega_p^{,2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2333.png"
 ALT="\begin{displaymath}
\omega^2 = k^2 c^2+\omega_p^{ 2}
\end{displaymath}">|; 

$key = q/displaystyle{{bf{A}-nablapsi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="$\displaystyle {\bf A} - \nabla\psi.$">|; 

$key = q/{displaymath}|{{bf{curl},{{bf{A}|=lim_{dSrightarrow0}frac{oint{{bf{A}cdotd{{bf{l}}{dS}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="\begin{displaymath}
\vert{\bf curl} {\bf A}\vert = \lim_{dS\rightarrow 0}\frac{\oint {\bf A}\cdot
d{\bf l}}{dS}
\end{displaymath}">|; 

$key = q/{{bf{r}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="${\bf r}_i$">|; 

$key = q/{{bf{B}_3=nablatimes{{bf{A}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1464.png"
 ALT="${\bf B}_3=\nabla\times{\bf A}_3$">|; 

$key = q/{displaymath}{{bf{B}({{bf{r})=frac{mu_0}{4pi}intfrac{{{bf{I}({{bf{r}')times({{bf{r}-{{bf{r}')}{|{{bf{r}-{{bf{r}'|^3},dl,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="\begin{displaymath}
{\bf B} ({\bf r}) = \frac{\mu_0}{4\pi} \int
\frac{{\bf I}({\...
...mes
({\bf r} - {\bf r}')}{\vert{\bf r} - {\bf r}'\vert^3} dl,
\end{displaymath}">|; 

$key = q/B_g=mu_0,H_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1839.png"
 ALT="$B_g=\mu_0 H_g$">|; 

$key = q/{{bf{E}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="${\bf E}_0$">|; 

$key = q/Q_0=Q+Q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="$Q_0= Q +Q'$">|; 

$key = q/{displaymath}{{bf{j}({{bf{r}),d^3{{bf{r}={{bf{I}({{bf{r}),dl,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="\begin{displaymath}
{\bf j}({\bf r}) d^3{\bf r} = {\bf I}({\bf r})  dl,
\end{displaymath}">|; 

$key = q/N({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1665.png"
 ALT="$N({\bf r})$">|; 

$key = q/Z_{{rm{in}simeqR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2094.png"
 ALT="$Z_{\rm in}\simeq R$">|; 

$key = q/{displaymath}oint{{bf{H}cdotd{{bf{l}=int{{bf{j}_tcdotd{{bf{S}=N,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1842.png"
 ALT="\begin{displaymath}
\oint {\bf H}\cdot d{\bf l} = \int{\bf j}_t\cdot d{\bf S} = N I.
\end{displaymath}">|; 

$key = q/partialslashpartialt=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="$\partial/\partial t=0$">|; 

$key = q/displaystyle-frac{partial}{partialt}left[epsilon_0,{{bf{E}times{{bf{B}right]_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2186.png"
 ALT="$\displaystyle -\frac{\partial}{\partial t} \left[\epsilon_0 {\bf E}\times{\bf B}\right]_i$">|; 

$key = q/{displaymath}oint_{S_i}{{bf{E}_3cdotd{{bf{S}_i=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1440.png"
 ALT="\begin{displaymath}
\oint_{S_i} {\bf E}_3 \cdot d{\bf S}_i = 0
\end{displaymath}">|; 

$key = q/lambda=cslashb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1529.png"
 ALT="$\lambda = c/b$">|; 

$key = q/{displaymath}B=mu_0,N,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1885.png"
 ALT="\begin{displaymath}
B= \mu_0  N  I.
\end{displaymath}">|; 

$key = q/{{bf{M}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1771.png"
 ALT="${\bf M}({\bf r})$">|; 

$key = q/{displaymath}{{bf{u}=frac{{{bf{E}times{{bf{B}}{mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3217.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{{\bf E}\times{\bf B}}{\mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}G^{ij}=-epsilon_0,E^iE^j-frac{B^iB^j}{mu_0}+delta^{ij},frac{1}{2}!left(epsilon_0,E^2+frac{B^2}{mu_0}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3221.png"
 ALT="\begin{displaymath}
G^{ij} = -\epsilon_0  E^i E^j - \frac{B^i B^j}{\mu_0}
+\del...
...frac{1}{2} \!\left(\epsilon_0  E^2 +\frac{B^2}{\mu_0}\right),
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{E}=frac{rho}{epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf E} = \frac{\rho}{\epsilon_0}
\end{displaymath}">|; 

$key = q/displaystylefrac{u'_2}{gamma,(1+u'_1,vslashc^2)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2751.png"
 ALT="$\displaystyle \frac{u'_2}{\gamma (1+u'_1  v/c^2)},$">|; 

$key = q/{displaymath}W=frac{4pi}{3,epsilon_0},rho^2int_0^ar^4,dr=frac{4pi}{15,epsilon_0},rho^2,a^5.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="\begin{displaymath}
W = \frac{4\pi}{3 \epsilon_0}  \rho^2 \int_0^a r^4 dr =
\frac{4\pi}{15 \epsilon_0}  \rho^2  a^5.
\end{displaymath}">|; 

$key = q/T^mu,dS_mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3291.png"
 ALT="$T^\mu dS_\mu$">|; 

$key = q/displaystyleA_y({{bf{r})=frac{mu_0}{4pi}intfrac{j_y({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="$\displaystyle A_y({\bf r}) = \frac{\mu_0}{4\pi} \int \frac{j_y({\bf r}')}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r}',$">|; 

$key = q/{{bf{r}=(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="${\bf r} = (x, y, z)$">|; 

$key = q/{displaymath}frac{d^2phi}{dx^2}=-frac{rho(x)}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1475.png"
 ALT="\begin{displaymath}
\frac{d^2\phi}{dx^2} = - \frac{\rho(x)}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}ksimeqsqrt{{{rm{i},mu_0,sigma,omega}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img2407.png"
 ALT="\begin{displaymath}
k\simeq \sqrt{{\rm i} \mu_0 \sigma \omega}.
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{E}=-frac{partial{{bf{B}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="\begin{displaymath}
\nabla\times{\bf E} = - \frac{\partial {\bf B}}{\partial t}.
\end{displaymath}">|; 

$key = q/beta=vslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2888.png"
 ALT="$\beta = v/c$">|; 

$key = q/{{bf{A}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1869.png"
 ALT="${\bf A}_1$">|; 

$key = q/{displaymath}{{bf{B}_i,{{rm{e}^{,{{rm{i},({{bf{k}_icdot{{bf{r}-omega,t)}+{{bf{B}{rm{e}^{,{{rm{i},({{bf{k}_tcdot{{bf{r}-omega,t)}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2501.png"
 ALT="\begin{displaymath}
{\bf B}_i {\rm e}^{ {\rm i} ({\bf k}_i\cdot{\bf r}-\omeg...
...f B}_t {\rm e}^{ {\rm i} ({\bf k}_t\cdot{\bf r}-\omega t)}
\end{displaymath}">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$S$">|; 

$key = q/{displaymath}sigma=-epsilon_0frac{partialphi_{{rm{analogue}(z=0_+)}{partialz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1498.png"
 ALT="\begin{displaymath}
\sigma = - \epsilon_0 \frac{\partial\phi_{\rm analogue}(z=0_+)}{\partial z}.
\end{displaymath}">|; 

$key = q/dW={{bf{F}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$dW={\bf F}\cdot d{\bf l}$">|; 

$key = q/{displaymath}frac{dP}{d{mitOmega}}=frac{e^4,E_0^{,2}}{32pi^2,epsilon_0,c^3,m_e^{,2}},sin^2theta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2278.png"
 ALT="\begin{displaymath}
\frac{dP}{d{\mit\Omega}} = \frac{e^4 E_0^{ 2}}{32\pi^2 \epsilon_0 c^3 m_e^{ 2}} \sin^2\theta.
\end{displaymath}">|; 

$key = q/{displaymath}r'=-c,t'=-c,gamma,left(t-frac{v,x}{c^2}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2989.png"
 ALT="\begin{displaymath}
r' = -c t' =- c \gamma \left(t - \frac{v x}{c^2}\right),
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig23.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig23.eps}}
\end{figure}">|; 

$key = q/displaystyle-frac{e}{4pi,epsilon_0}frac{gamma}{r^3,(1+u_r^{~2},gamma^2slashc^2)^{3slash2}},{{bf{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3141.png"
 ALT="$\displaystyle - \frac{e}{4\pi \epsilon_0} \frac{\gamma}{r^3 
(1+ u_r^{&nbsp;2}  \gamma^2/c^2)^{3/2}} {\bf r},$">|; 

$key = q/p=gamma,m_0,u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3322.png"
 ALT="$p= \gamma  m_0  u$">|; 

$key = q/P_{{rm{in}=P_{{rm{load}+P_{{rm{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2250.png"
 ALT="$P_{\rm in} = P_{\rm load} + P_{\rm rad}$">|; 

$key = q/n_e,B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2392.png"
 ALT="$n_e B_0$">|; 

$key = q/dt'^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2684.png"
 ALT="$dt'^2$">|; 

$key = q/{displaymath}F^{4i}=-E^i=frac{e,gamma}{4pi,epsilon_0,{r'}^3},r^i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img3137.png"
 ALT="\begin{displaymath}
F^{4i} = -E^i = \frac{e \gamma}{4\pi \epsilon_0 {r'}^3} r^i,
\end{displaymath}">|; 

$key = q/{displaymath}R_{{rm{rad}=frac{2.44}{4pi,epsilon_0,c}=73,,{{rm{ohms}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2243.png"
 ALT="\begin{displaymath}
R_{\rm rad} = \frac{ 2.44}{4\pi  \epsilon_0  c} = 73   {\rm ohms}.
\end{displaymath}">|; 

$key = q/{displaymath}V=int!intD(x,y),dS.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="\begin{displaymath}
V= \int\!\int D(x,y) dS.
\end{displaymath}">|; 

$key = q/9.1times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$9.1\times 10^{-31}$">|; 

$key = q/{displaymath}r(x^i,{x^i}')=left[(x^i-{x^i}'),(x_i-{x_i}')right]^{1slash2}=c,(t-t').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img3233.png"
 ALT="\begin{displaymath}
r(x^i, {x^i}') = \left[ (x^i-{x^i}') (x_i-{x_i}')\right]^{1/2} = c (t-t').
\end{displaymath}">|; 

$key = q/k_{i,y}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2508.png"
 ALT="$k_{i y}=0$">|; 

$key = q/{mitPhi}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1988.png"
 ALT="${\mit\Phi}_i$">|; 

$key = q/{displaymath}V=I,R+L,frac{dI}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1895.png"
 ALT="\begin{displaymath}
V = I R + L  \frac{dI}{dt}.
\end{displaymath}">|; 

$key = q/displaystylefrac{partialE_z}{partialy}-{{rm{i},k,E_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2578.png"
 ALT="$\displaystyle \frac{\partial E_z}{\partial y} - {\rm i} k E_y,$">|; 

$key = q/{displaymath}theta_{{rm{max}=cos^{-1}left[frac{1}{3,uslashc}(sqrt{1+15,u^2slashc^2}-1)right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3348.png"
 ALT="\begin{displaymath}
\theta_{\rm max} = \cos^{-1} \left[ \frac{1}{3  u/c}(\sqrt{1+ 15  u^2/c^2}
- 1)\right].
\end{displaymath}">|; 

$key = q/dhslashdl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$dh/dl$">|; 

$key = q/lambda=0.76;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="$\lambda= 0.76$">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{l}=mu_0int_S{{bf{j}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="\begin{displaymath}
\oint_C {\bf B} \cdot d{\bf l} = \mu_0 \int_S {\bf j} \cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$u$">|; 

$key = q/{displaymath}langle{{bf{u}rangle=frac{omega^2,l^2,I_0^{,2}}{32pi^2,epsilon_0,c^3},frac{sin^2theta}{r^2},hat{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2230.png"
 ALT="\begin{displaymath}
\langle {\bf u}\rangle = \frac{\omega^2  l^2  I_0^{ 2}}{3...
..., \epsilon_0  c^3}  \frac{\sin^2\theta}
{r^2}  \hat{\bf r}.
\end{displaymath}">|; 

$key = q/partialE_zslashpartialz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$\partial E_z/\partial z$">|; 

$key = q/{displaymath}{{bf{h}=-kappa,,{{bf{grad},T,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="\begin{displaymath}
{\bf h} = - \kappa   {\bf grad} T,
\end{displaymath}">|; 

$key = q/{displaymath}n,{{bf{a}equiv(n,a_x,n,a_y,n,a_z){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="\begin{displaymath}
n {\bf a} \equiv (n a_x,n a_y, n a_z)
\end{displaymath}">|; 

$key = q/{displaymath}overline{z}=left.int!int!intz,dVrightslashint!int!intdV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="\begin{displaymath}
\overline{z} = \left. \int\!\int\!\int z dV\right/ \int\!\int\!\int dV.
\end{displaymath}">|; 

$key = q/Box^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="$\Box^2$">|; 

$key = q/F(z)=U(x,y)+{{rm{i},V(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1580.png"
 ALT="$F(z)=U(x,y) + {\rm i} V(x,y)$">|; 

$key = q/n=sqrt{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2327.png"
 ALT="$n=\sqrt{\epsilon}$">|; 

$key = q/A_{klm}^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2813.png"
 ALT="$A_{klm}^{ij}$">|; 

$key = q/{displaymath}M=sqrt{L_1,L_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img1915.png"
 ALT="\begin{displaymath}
M = \sqrt{L_1  L_2}.
\end{displaymath}">|; 

$key = q/q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$q_i$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig39.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="342" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="\begin{figure}
\epsfysize =3 in
\centerline{\epsffile{fig39.eps}}
\end{figure}">|; 

$key = q/{displaymath}L=frac{{mitPhi}}{I}=mu_0,N^2,pi,r^2,l.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1889.png"
 ALT="\begin{displaymath}
L = \frac{{\mit\Phi}}{I} = \mu_0  N^2  \pi  r^2  l.
\end{displaymath}">|; 

$key = q/gamma^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3381.png"
 ALT="$\gamma^6$">|; 

$key = q/{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="${\bf E}$">|; 

$key = q/B_{ijk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2809.png"
 ALT="$B_{ijk}$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{S}={{bf{A}cdotointd{{bf{S}={{bf{A}cdot{{bf{S}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf S} = {\bf A}\cdot \oint d{\bf S} = {\bf A} \cdot {\bf S}=0,
\end{displaymath}">|; 

$key = q/Vslashl=E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="$V/l = E_z$">|; 

$key = q/F(z)=z^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1548.png"
 ALT="$F(z) = z^2$">|; 

$key = q/rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2960.png"
 ALT="$\rho_0$">|; 

$key = q/{displaymath}{mitPhi}^mu=frac{1}{4pi,epsilon_0,c}intfrac{[J^mu]}{r},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2984.png"
 ALT="\begin{displaymath}
{\mit \Phi}^\mu = \frac{1}{4\pi \epsilon_0 c}\int
\frac{[J^\mu]}
{ r} dV.
\end{displaymath}">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1625.png"
 ALT="$k$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig40.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig40.eps}}
\end{figure}">|; 

$key = q/displaystylefrac{v_perp}{mitOmega},cos({mitOmega},t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$\displaystyle \frac{v_\perp}{\mit\Omega} \cos({\mit\Omega} t),$">|; 

$key = q/k_r=n,omegaslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2404.png"
 ALT="$k_r = n \omega/c$">|; 

$key = q/displaystyleG_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3077.png"
 ALT="$\displaystyle G_{ij}$">|; 

$key = q/{displaymath}Z_{{rm{in}={{rm{i},Z_0tan(k,l-pislash2).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2090.png"
 ALT="\begin{displaymath}
Z_{\rm in} = {\rm i} Z_0\tan(k l-\pi/2).
\end{displaymath}">|; 

$key = q/{displaymath}phi(x,y,z)=-E_0,U(x,y)=-E_0,x+E_0,c^2,frac{x}{x^2+y^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1586.png"
 ALT="\begin{displaymath}
\phi(x,y,z) = - E_0 U(x,y) = -E_0 x + E_0 c^2 \frac{x}{x^2+y^2}
\end{displaymath}">|; 

$key = q/{calI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="${\cal I}$">|; 

$key = q/{displaymath}A^mu=frac{dU^mu}{dtau}=gamma,frac{dU^mu}{dt}=gammafrac{d}{dt}(gamma,{{bf{u}+gamma,{{bf{a},c,frac{dgamma}{dt}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2946.png"
 ALT="\begin{displaymath}
A^\mu = \frac{dU^\mu}{d\tau} = \gamma \frac{dU^\mu}{dt}
=\g...
...dt}  {\bf u} + \gamma {\bf a}, c \frac{d\gamma}{dt}\right),
\end{displaymath}">|; 

$key = q/dE=U,dV=(epsilon_0slash2),E^2,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="$dE = U dV = (\epsilon_0/2)  E^2
 dV$">|; 

$key = q/dx';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2661.png"
 ALT="$dx'$">|; 

$key = q/displaystylefrac{q}{4pi,epsilon_0}frac{{{bf{r}-{{bf{r}_0}{|{{bf{r}-{{bf{r}_0|^3}box{hspace{1cm}for,{t_1leqt-|{{bf{r}-{{bf{r}_0|slashcleqt_2{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="$\displaystyle \frac{q}{4\pi  \epsilon_0} \frac{{\bf r} - {\bf r}_0}{\vert{\bf ...
...\mbox{\hspace{1cm} for  $ t_1\leq t-\vert{\bf r} - {\bf r}_0\vert/c \leq t_2$}$">|; 

$key = q/displaystyle-nablaphi-frac{partial{{bf{A}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="$\displaystyle - \nabla\phi - \frac{\partial {\bf A}}{\partial t},$">|; 

$key = q/phi(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1477.png"
 ALT="$\phi(0)=0$">|; 

$key = q/displaystyle{T^i}_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3200.png"
 ALT="$\displaystyle {T^i}_4$">|; 

$key = q/displaystylefrac{partialx^{i'}}{partialx^i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2782.png"
 ALT="$\displaystyle \frac{\partial x^{i'}}{\partial x^i}$">|; 

$key = q/{displaymath}W_B=frac{1}{2},L_1,I_1^{,2}+frac{1}{2},L_2,I_2^{,2}+M,I_1,I_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1965.png"
 ALT="\begin{displaymath}
W_B = \frac{1}{2}  L_1  I_1^{ 2} + \frac{1}{2}  L_2  I_2^{ 2} + M  I_1  I_2.
\end{displaymath}">|; 

$key = q/{displaymath}G({{bf{r},{{bf{r}')=-frac{1}{4pi}frac{1}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="\begin{displaymath}
G({\bf r}, {\bf r}') = -\frac{1}{4\pi} \frac{1}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot(phi_3,nablaphi_3)equiv(nablaphi_3)^2+phi_3nabla^2phi_3.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1411.png"
 ALT="\begin{displaymath}
\nabla\cdot(\phi_3 \nabla\phi_3) \equiv (\nabla \phi_3)^2 +\phi_3\nabla^2\phi_3.
\end{displaymath}">|; 

$key = q/c,B^{ij}rightarrowE^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3073.png"
 ALT="$c B^{ij} \rightarrow E^{ij}$">|; 

$key = q/{displaymath}epsilon^{ijk},partial_j(c,B_k)-partial_4E^i=epsilon^{ijk},partial_j,B^{ab})+partial_4F^{4i}=frac{J^i}{c,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="471" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3051.png"
 ALT="\begin{displaymath}
\epsilon^{ijk}  \partial_j( c B_k) - \partial_4 E^i
= \ep...
... c  B^{ab} )
+ \partial_4 F^{4i} = \frac{J^i}{c \epsilon_0}.
\end{displaymath}">|; 

$key = q/mu';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2923.png"
 ALT="$\mu'$">|; 

$key = q/{displaymath}{{rm{i},{{bf{k}times{{bf{B}_0=-{{rm{i},epsilon_0mu_0,omega,{{bf{E}_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="\begin{displaymath}
{\rm i}  {\bf k}\times{\bf B}_0 = -{\rm i} \epsilon_0\mu_0  \omega 
{\bf E}_0.
\end{displaymath}">|; 

$key = q/{displaymath}-frac{partial}{partialt}!int_VU,dV=oint_S{{bf{u}cdotd{{bf{S}+int_V{{bf{E}cdot{{bf{j},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2114.png"
 ALT="\begin{displaymath}
-\frac{\partial}{\partial t} \!\int_V U dV= \oint_S {\bf u}\cdot d{\bf S}
+ \int_V {\bf E}\cdot{\bf j} dV.
\end{displaymath}">|; 

$key = q/Bsim10^{-9};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="$B\sim 10^{-9}$">|; 

$key = q/theta_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2493.png"
 ALT="$\theta_t$">|; 

$key = q/dq=-[partialP_x(x,y,z)slashpartialx+partialP_y(x,y,z)slashpartialy+partialP_z(x,y,z)slashpartialz],dx,dy,dz=-(nabla!cdot!{{bf{P}),dx,dy,dz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="720" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1670.png"
 ALT="$dq = - [\partial P_x(x,y,z)/\partial x+ \partial P_y(x,y,z)/\partial y+\partial P_z(x,y,z)/\partial z] 
dx dy dz = - (\nabla\!\cdot\!{\bf P}) dx dy dz.$">|; 

$key = q/displaystyle(a_x^{~2}+a_y^{~2}+a_z^{~2}),(b_x^{~2}+b_y^{~2}+b_z^{~2})-(a_x,b_x+a_y,b_y+a_z,b_z)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle (a_x^{&nbsp;2}+a_y^{&nbsp;2}+a_z^{&nbsp;2}) (b_x^{&nbsp;2}+b_y^{&nbsp;2}+b_z^{&nbsp;2}) -
(a_x  b_x + a_y  b_y + a_z  b_z)^2$">|; 

$key = q/{{bf{r'}=(x',,y',,z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="${\bf r'}= (x', y', z')$">|; 

$key = q/{displaymath}V=frac{Q}{4pi,epsilon_0,a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="\begin{displaymath}
V = \frac{Q}{4\pi  \epsilon_0  a}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{l}{c}llfrac{2pi}{omega},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2215.png"
 ALT="\begin{displaymath}
\frac{l}{c} \ll \frac{2\pi}{\omega},
\end{displaymath}">|; 

$key = q/x,y,zrightarrow-x,-y,-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2852.png"
 ALT="$x,y,z\rightarrow -x,-y,-z$">|; 

$key = q/{displaymath}W=frac{1}{2}int{{bf{E}!cdot!{{bf{D},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1764.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \int {\bf E}\!\cdot\!{\bf D} d^3{\bf r}.
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{E}={{bf{0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="\begin{displaymath}
\nabla\times{\bf E} = {\bf0}.
\end{displaymath}">|; 

$key = q/partialB_zslashpartialy=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2611.png"
 ALT="$\partial B_z/\partial y=0$">|; 

$key = q/theta_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3347.png"
 ALT="$\theta_{\rm max}$">|; 

$key = q/{displaymath}V_2=V_1,k,sqrt{frac{L_2}{L_1}},exp(-R_1,tslashL_1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1934.png"
 ALT="\begin{displaymath}
V_2 = V_1  k  \sqrt{\frac{L_2}{L_1}}  \exp(- R_1  t/L_1).
\end{displaymath}">|; 

$key = q/displaystyleE_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2474.png"
 ALT="$\displaystyle E_t$">|; 

$key = q/phisimeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3392.png"
 ALT="$\phi \simeq 0$">|; 

$key = q/{displaymath}F_z=-frac{1}{4pi,epsilon_0}frac{q^2}{4,z^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1516.png"
 ALT="\begin{displaymath}
F_z = - \frac{1}{4\pi  \epsilon_0} \frac{q^2}{4  z^2}.
\end{displaymath}">|; 

$key = q/G({{bf{r},{{bf{r}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="$G({\bf r}, {\bf r}')$">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}left(oint_Sphi,{{bf{E}cdotd{{bf{S}+int_VE^2,dVright),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \left(\oint_S \phi {\bf E} \cdot d{\bf S}+
\int_V E^2 dV\right),
\end{displaymath}">|; 

$key = q/[F({{bf{r},t)]equivF({{bf{r},t_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="$[F({\bf r}, t)]\equiv F({\bf r}, t_r)$">|; 

$key = q/{mitPhi}_2=M,I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1911.png"
 ALT="${\mit\Phi}_2
=M  I_1$">|; 

$key = q/displaystylefrac{E_r}{v_1},left(costheta_i,,0,,sintheta_iright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2529.png"
 ALT="$\displaystyle \frac{E_r}{v_1} \left(\cos\theta_i, 0, \sin\theta_i\right),$">|; 

$key = q/{displaymath}dq=4pi,r^2,rho,dr.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="\begin{displaymath}
dq = 4\pi  r^2  \rho dr.
\end{displaymath}">|; 

$key = q/{displaymath}ds^2={dx'}^2+{dy'}^2+{dz'}^2-c^2,{dt'}^2={dx}^2+{dy}^2+{dz}^2-c^2,{dt}^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2914.png"
 ALT="\begin{displaymath}
ds^2 = {dx'}^2 + {dy'}^2 + {dz'}^2 - c^2  {dt'}^2 =
{dx}^2 + {dy}^2 + {dz}^2 - c^2  {dt}^2,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}rightarrow{{bf{E}~~~{{rm{as}~~~phirightarrowphi+c.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="\begin{displaymath}
{\bf E} \rightarrow {\bf E}&nbsp;&nbsp;&nbsp;{\rm as}&nbsp;&nbsp;&nbsp;\phi\rightarrow \phi + c.
\end{displaymath}">|; 

$key = q/{displaymath}U(x,y)=x-frac{c^2,x}{x^2+y^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1581.png"
 ALT="\begin{displaymath}
U(x,y) = x - \frac{c^2 x}{x^2+y^2}.
\end{displaymath}">|; 

$key = q/K=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2086.png"
 ALT="$K= -1$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}=frac{e^2,dot{u}^{2}}{16pi^2,epsilon_0,c^3}frac{sin^2theta}{[1-(uslashc),costheta]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3343.png"
 ALT="\begin{displaymath}
\frac{d P(t')}{d{\mit\Omega}} = \frac{e^2 \dot{u}^{2}}{16\p...
...epsilon_0  c^3} \frac{\sin^2\theta}{[1-(u/c) \cos\theta]^5}.
\end{displaymath}">|; 

$key = q/{displaymath}epsilon=1-frac{omega_p^{,2}}{omega^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2325.png"
 ALT="\begin{displaymath}
\epsilon = 1 - \frac{\omega_p^{ 2}}{\omega^2},
\end{displaymath}">|; 

$key = q/p_{mu}^{nu'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2930.png"
 ALT="$p_{\mu}^{\nu'}$">|; 

$key = q/phi(d)=V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1478.png"
 ALT="$\phi(d)=V_0$">|; 

$key = q/A_{k'cdotsl',m'}^{i'cdotsj'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2827.png"
 ALT="$A_{k'\cdots l', m'}^{i'\cdots j'}$">|; 

$key = q/{displaymath}F'=F+R=({{rm{retarded}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="\begin{displaymath}
F' = F+R = ({\rm retarded}).
\end{displaymath}">|; 

$key = q/B_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1829.png"
 ALT="$B_1$">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0,c^2}frac{{{bf{r}times({{bf{r}timesdot{{bf{u})}{r^3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3275.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0  c^2} \frac{{\bf r}\times
({\bf r}\times\dot{\bf u})}{r^3},$">|; 

$key = q/displaystyleT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2487.png"
 ALT="$\displaystyle T$">|; 

$key = q/mu_0,{{bf{j}=nablatimes{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1995.png"
 ALT="$\mu_0  {\bf j} = \nabla\times {\bf B}$">|; 

$key = q/{displaymath}nablacdot{{bf{A}=-epsilon_0mu_0,frac{partialphi}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf A} = -\epsilon_0 \mu_0  \frac{\partial \phi}{\partial t}.
\end{displaymath}">|; 

$key = q/c,g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2157.png"
 ALT="$c g$">|; 

$key = q/{{bf{B}=B_0,hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2352.png"
 ALT="${\bf B} = B_0 \hat{\bf z}$">|; 

$key = q/{{bf{B}_1+{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="${\bf B}_1+{\bf B}_2$">|; 

$key = q/{displaymath}{{bf{r}=s_+,{{rm{e}^{,{{rm{i},(k_+,z-omega,t)},{{bf{e}_++s_-,{{rm{e}^{,{{rm{i},(k_-,z-omega,t)},{{bf{e}_-,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2366.png"
 ALT="\begin{displaymath}
{\bf r} = s_+ {\rm e}^{ {\rm i} (k_+ z-\omega t)} {\bf e}_+
+ s_- {\rm e}^{ {\rm i} (k_- z-\omega t)} {\bf e}_-,
\end{displaymath}">|; 

$key = q/{displaymath}phi(r,theta)=r^{m}costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1648.png"
 ALT="\begin{displaymath}
\phi(r, \theta) = r^{m}\cos\theta.
\end{displaymath}">|; 

$key = q/E^2(x,y,z)=E^2(x,y,-z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1509.png"
 ALT="$E^2(x, y, z) = E^2(x, y, -z)$">|; 

$key = q/(d_1,d_2,d_3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2695.png"
 ALT="$(d_1, d_2, d_3)$">|; 

$key = q/{displaymath}[f]=f({{bf{r}',t-|{{bf{r}-{{bf{r}'|slashc).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2204.png"
 ALT="\begin{displaymath}[f]= f({\bf r}', t - \vert{\bf r} - {\bf r}'\vert/c).
\end{displaymath}">|; 

$key = q/dV'slashr'=dVslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2997.png"
 ALT="$dV'/r' = dV/r$">|; 

$key = q/{displaymath}Q=int_{x-y,{rm{plane}sigma,dS,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1501.png"
 ALT="\begin{displaymath}
Q = \int_{x-y  \rm plane} \sigma dS,
\end{displaymath}">|; 

$key = q/{displaymath}tau=frac{L}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1903.png"
 ALT="\begin{displaymath}
\tau = \frac{L}{R}.
\end{displaymath}">|; 

$key = q/{displaymath}V=L,frac{dL}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2003.png"
 ALT="\begin{displaymath}
V = L  \frac{dL}{dt},
\end{displaymath}">|; 

$key = q/A^i=C^{ij}B_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2822.png"
 ALT="$A^i = C^{ij} B_j$">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intrho({{bf{r}'),nablacdotleft(frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3}right),d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="$\displaystyle \frac{1}{4\pi \epsilon_0}\int
\rho({\bf r}') \nabla\cdot\left(\frac{{\bf r} - {\bf r}'}
{\vert{\bf r} - {\bf r}'\vert^3}\right) d^3{\bf r}'$">|; 

$key = q/B_perp,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="$B_\perp A$">|; 

$key = q/{displaymath}frac{partialI}{partialx}=-C,frac{partialV}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2051.png"
 ALT="\begin{displaymath}
\frac{\partial I}{\partial x} = - C \frac{\partial V}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=a_x,b_x+a_y,b_y+a_z,b_z={{rm{scalar~number}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = a_x  b_x + a_y  b_y + a_z  b_z = {\rm scalar&nbsp;number}.
\end{displaymath}">|; 

$key = q/{displaymath}f_nu=epsilon_0left[partial_mu(F^{musigma}F_{nusigma})-frac{1}{4},partial_nu(F^{musigma}F_{musigma})right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3194.png"
 ALT="\begin{displaymath}
f_\nu =\epsilon_0 \left[\partial_\mu(F^{\mu\sigma}F_{\nu\sig...
...frac{1}{4}  \partial_\nu (F^{\mu\sigma}F_{\mu\sigma})\right].
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=a_x^{~2}+a_y^{~2}+a_z^{~2}={{rm{Length}~(OP)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} = a_x^{&nbsp;2}+a_y^{&nbsp;2} + a_z^{&nbsp;2} = {\rm Length}&nbsp;(OP)^2,
\end{displaymath}">|; 

$key = q/infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$\infty$">|; 

$key = q/R_mu,Q^mu=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2904.png"
 ALT="$R_\mu  Q^\mu = 0$">|; 

$key = q/{displaymath}nablatimes{{bf{H}={{bf{j}_t+frac{partial{{bf{D}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1781.png"
 ALT="\begin{displaymath}
\nabla\times{\bf H} = {\bf j}_t + \frac{\partial{\bf D}}{\partial t},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{D}=epsilon_0,epsilon,{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1683.png"
 ALT="\begin{displaymath}
{\bf D} = \epsilon_0 \epsilon {\bf E},
\end{displaymath}">|; 

$key = q/{displaymath}{calF}^mu=frac{dP^mu}{dtau}=m_0,A^mu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3166.png"
 ALT="\begin{displaymath}
{\cal F}^\mu = \frac{dP^\mu}{d\tau} = m_0  A^\mu,
\end{displaymath}">|; 

$key = q/displaystyle{{rm{i}left(-frac{omega}{c^2},nablaE_ztimeshat{{bf{z}+k,nablaB_zright)left(frac{omega^2}{c^2}-k^2right)^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2594.png"
 ALT="$\displaystyle {\rm i}\left(-\frac{\omega}{c^2} \nabla E_z\times\hat{\bf z} + k \nabla
B_z\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1}.$">|; 

$key = q/{displaymath}x^2+frac{2,(c-lambda,b)}{lambda-1},x+y^2+z^2=frac{c^2-lambda,b^2}{lambda-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1526.png"
 ALT="\begin{displaymath}
x^2 + \frac{2 (c-\lambda b)}{\lambda-1}  x + y^2 + z^2 = \frac{c^2-\lambda b^2}{\lambda-1},
\end{displaymath}">|; 

$key = q/F'(phi)=dF(phi)slashdphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="$F'(\phi) = d F(\phi)/d\phi$">|; 

$key = q/displaystyleG^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3066.png"
 ALT="$\displaystyle G^{ij}$">|; 

$key = q/{mitPhi}_mu=(-c,{{bf{A},phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3021.png"
 ALT="${\mit\Phi}_\mu = (-c {\bf A}, \phi)$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="$j$">|; 

$key = q/{displaymath}nablacdot{{bf{A}=frac{1}{r}frac{partial(rA_r)}{partialr}+frac{1}{r}_theta}{partialtheta}+frac{partialA_z}{partialz}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf A} = \frac{1}{r}\frac{\partial (r A_r)}{\pa...
...l A_\theta}{\partial \theta} + \frac{\partial A_z}{\partial z}
\end{displaymath}">|; 

$key = q/uslashcrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3143.png"
 ALT="$u/c\rightarrow 0$">|; 

$key = q/{displaymath}K=frac{R-Z_0}{R+Z_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2081.png"
 ALT="\begin{displaymath}
K = \frac{ R - Z_0}{R+Z_0}.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intleft(frac{rho,{{bf{R}}{R^3}-frac{1}{2}frac{^2R}-frac{partial{{bf{j}slashpartialt}{c^2R}+cdotsright),dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int \left(
\frac{\rho {\bf R}}{R^3}...
...c{\bf R}{c^2 R} - \frac{\partial {\bf j}/\partial t}{c^2 R}+\cdots\right) dV',$">|; 

$key = q/-k^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1613.png"
 ALT="$-k^2$">|; 

$key = q/+q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1385.png"
 ALT="$+q$">|; 

$key = q/phi_1=phi_2=phi_3=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1443.png"
 ALT="$\phi_1=\phi_2 = \phi_3 =0$">|; 

$key = q/P=(x_0,,y_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$P=(x_0,  y_0)$">|; 

$key = q/p_0=q_0,l=I_0,lslashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2264.png"
 ALT="$p_0= q_0 l=I_0 l/\omega$">|; 

$key = q/{displaymath}V_0,cos(omega,t)=I_0,cos(omega,t),(R_{{rm{rad}+R_{{rm{load}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2246.png"
 ALT="\begin{displaymath}
V_0  \cos(\omega  t) = I_0  \cos(\omega  t)  (R_{\rm rad} + R_{\rm load}),
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{j}_p=frac{partial{{bf{P}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1776.png"
 ALT="\begin{displaymath}
{\bf j}_p = \frac{\partial{\bf P}}{\partial t}.
\end{displaymath}">|; 

$key = q/rrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2649.png"
 ALT="$r\rightarrow 0$">|; 

$key = q/delta{{bf{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1756.png"
 ALT="$\delta{\bf D}$">|; 

$key = q/{displaymath}{{bf{v}=frac{d{{bf{r}}{dt}=lim_{deltatrightarrow0}frac{{{bf{r}(t+deltat)-{{bf{r}(t)}{deltat}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\begin{displaymath}
{\bf v} = \frac{d {\bf r}}{dt} = \lim_{\delta t\rightarrow 0}
\frac{ {\bf r}(t+\delta t) - {\bf r}(t) }{\delta t}.
\end{displaymath}">|; 

$key = q/F_x(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="$F_x(\phi)$">|; 

$key = q/{displaymath}frac{partialE_x}{partialx}=frac{q}{4pi,epsilon_0}left(frac{1}{r^3}-ght)=frac{q}{4pi,epsilon_0}frac{r^2-3,x^2}{r^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="\begin{displaymath}
\frac{\partial E_x}{\partial x} = \frac{q}{4\pi \epsilon_0}...
...r} \right) =
\frac{q}{4\pi \epsilon_0}\frac{r^2-3 x^2}{r^5}.
\end{displaymath}">|; 

$key = q/{displaymath}f(x)=g(y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1609.png"
 ALT="\begin{displaymath}
f(x) = g(y),
\end{displaymath}">|; 

$key = q/displaystylefrac{dx'}{dt'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2737.png"
 ALT="$\displaystyle \frac{dx'}{dt'},$">|; 

$key = q/{{bf{curl},{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="${\bf curl} {\bf A}
\cdot d{\bf S}$">|; 

$key = q/[partialrhoslashpartialt]=-[nablacdot{{bf{j}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="$[\partial \rho/\partial t] = -[\nabla\cdot {\bf j}]$">|; 

$key = q/{displaymath}{mitDelta}tsimeqfrac{{mitDelta}theta}{2,omega_0,gamma^2}simfrac{1}{omega_0,gamma^3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3398.png"
 ALT="\begin{displaymath}
{\mit\Delta} t \simeq \frac{{\mit\Delta}\theta}{2 \omega_0  \gamma^2} \sim
\frac{1}{\omega_0 \gamma^3},
\end{displaymath}">|; 

$key = q/(x^1,x^2,x^3,x^4);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2873.png"
 ALT="$(x^1, x^2, x^3, x^4)$">|; 

$key = q/{displaymath}E_i-E_r=frac{v_1}{v_2},E_t=frac{n_2}{n_1},E_t,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img2470.png"
 ALT="\begin{displaymath}
E_i - E_r = \frac{v_1}{v_2} E_t = \frac{n_2}{n_1} E_t,
\end{displaymath}">|; 

$key = q/{displaymath}Z_{{rm{in}=frac{V(-l,t)}{I(-l,t)}=Z_0,frac{R,cos(k,l)+{{rm{i},Z_0,sin(k,l)}{Z_0,cos(k,l)+{{rm{i},R,sin(k,l)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="370" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2082.png"
 ALT="\begin{displaymath}
Z_{\rm in} = \frac{V(-l, t)}{I(-l, t)} = Z_0  \frac{R  \co...
...,\sin( k l)}
{Z_0  \cos (k l) + {\rm i}  R  \sin (k l)}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=1.75in{centerline{epsffile{fig19.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="199" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="\begin{figure}
\epsfysize =1.75in
\centerline{\epsffile{fig19.eps}}
\end{figure}">|; 

$key = q/{{bf{u}timesdot{{bf{u}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3355.png"
 ALT="${\bf u}\times\dot{\bf u}
= 0$">|; 

$key = q/displaystyleF_y[,k,(r-c,t),],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="$\displaystyle F_y [ k (r-c t) ],$">|; 

$key = q/displaystyleepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="$\displaystyle \epsilon_0$">|; 

$key = q/{displaymath}{{bf{a}+{{bf{b}equiv(a_x+b_x,,a_y+b_y,,a_z+b_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="\begin{displaymath}
{\bf a} + {\bf b} \equiv (a_x+b_x,  a_y+b_y,  a_z+b_z).
\end{displaymath}">|; 

$key = q/{displaymath}L=frac{{mitPhi}}{I}=frac{mu_0}{2pi}ln(bslasha).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2069.png"
 ALT="\begin{displaymath}
L = \frac{{\mit\Phi}}{I} = \frac{\mu_0}{2\pi} \ln(b/a).
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2},L,I^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1970.png"
 ALT="\begin{displaymath}
W = \frac{1}{2}  L  I^2,
\end{displaymath}">|; 

$key = q/{{bf{P}=N,{{bf{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1658.png"
 ALT="${\bf P} = N  {\bf p}$">|; 

$key = q/z=-lslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2205.png"
 ALT="$z=-l/2$">|; 

$key = q/y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1593.png"
 ALT="$y=0$">|; 

$key = q/{displaymath}Mleqsqrt{L_1,L_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img1969.png"
 ALT="\begin{displaymath}
M \leq \sqrt{L_1  L_2}.
\end{displaymath}">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$G$">|; 

$key = q/{displaymath}W_i=frac{3}{5}frac{q_i^{,2}}{4pi,epsilon_0,a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="\begin{displaymath}
W_i = \frac{3}{5} \frac{q_i^{ 2}}{4\pi  \epsilon_0  a}.
\end{displaymath}">|; 

$key = q/cos^2(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2156.png"
 ALT="$\cos^2 (\omega  t)$">|; 

$key = q/{displaymath}f_i=e,(E_i+B_{ij},u^j),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3172.png"
 ALT="\begin{displaymath}
f_i = e (E_i + B_{ij}  u^j),
\end{displaymath}">|; 

$key = q/{displaymath}frac{4pi,epsilon_0}{e},{{bf{E}=frac{1}{s^3}left({{bf{r}-frac{r,{{bf{r,{{bf{u}}{c}right)timesdot{{bf{u}right]right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="537" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3256.png"
 ALT="\begin{displaymath}
\frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{1}{s^3} \left(...
...- \frac{r {\bf u}}{c}\right)\times\dot{\bf u}\right]
\right).
\end{displaymath}">|; 

$key = q/displaystyle{{rm{i}left(omega,nablaB_ztimeshat{{bf{z}+k,nablaE_zright)left(frac{omega^2}{c^2}-k^2right)^{-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2593.png"
 ALT="$\displaystyle {\rm i}\left(\omega \nabla B_z\times\hat{\bf z} + k \nabla
E_z\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1},$">|; 

$key = q/{displaymath}theta={{rm{arg}(Z)=tan^{-1}left(frac{omega,L-1slashomega,C}{R}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2034.png"
 ALT="\begin{displaymath}
\theta = {\rm arg}(Z) = \tan^{-1}\left( \frac{\omega  L - 1/\omega  C }
{R} \right).
\end{displaymath}">|; 

$key = q/R_0=c,t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="$R_0 = c  t_0$">|; 

$key = q/alpha_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\alpha_y$">|; 

$key = q/{displaymath}dx'=frac{partialF}{partialx},dx+frac{partialF}{partialy},dy+frac{patialF}{partialz},dz+frac{partialF}{partialt},dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2670.png"
 ALT="\begin{displaymath}
dx' = \frac{\partial F}{\partial x} dx +
\frac{\partial F...
...artial F}{\partial z} dz
+ \frac{\partial F}{\partial t} dt.
\end{displaymath}">|; 

$key = q/x_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="$x_i$">|; 

$key = q/1slashr^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1853.png"
 ALT="$1/r^5$">|; 

$key = q/{displaymath}sum_{n=1}^inftyC_nint_0^pisin(n,y),,sin(n',y),,dy=int_0^piphi_0(y),sin(n',y),,dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1635.png"
 ALT="\begin{displaymath}
\sum_{n=1}^\infty C_n \int_0^\pi \sin (n y)  \sin (n' y)  dy =
\int_0^\pi \phi_0(y) \sin( n'  y)   dy.
\end{displaymath}">|; 

$key = q/E_irightarrow-c,B_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3082.png"
 ALT="$E_i\rightarrow -c B_i$">|; 

$key = q/{displaymath}F_{4i}=partial_4{mitPhi}_i-partial_i{mitPhi}_4=E_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img3032.png"
 ALT="\begin{displaymath}
F_{4i} = \partial_4{\mit\Phi}_i -\partial_i{\mit\Phi}_4 = E_i.
\end{displaymath}">|; 

$key = q/{displaymath}int_Snablatimes{{bf{B}cdotd{{bf{S}=mu_0,Iintintdelta(x),delta(y),dx,dy{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="\begin{displaymath}
\int_S \nabla\times{\bf B} \cdot d{\bf S} = \mu_0  I \int\int
\delta(x) \delta(y)  dx dy
\end{displaymath}">|; 

$key = q/displaystylenabla^2W_y=-C_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="$\displaystyle \nabla^2 W_y = - C_y,$">|; 

$key = q/{displaymath}int_0^tI(x,t),dt-int_0^tI(x+deltax,t)=C,deltax,V(x,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2050.png"
 ALT="\begin{displaymath}
\int_0^t I(x, t) dt - \int_0^t I(x+\delta x, t) = C \delta x V(x,t),
\end{displaymath}">|; 

$key = q/{displaymath}langleu_{{rm{in}rangle=frac{epsilon_0,c,E_0^{,2}}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2255.png"
 ALT="\begin{displaymath}
\langle u_{\rm in}\rangle = \frac{\epsilon_0  c  E_0^{ 2}}{2},
\end{displaymath}">|; 

$key = q/{{bf{grad},h=(partialhslashpartialx,,partialhslashpartialy);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="${\bf grad} h = (\partial h/\partial x,  \partial h/\partial y)$">|; 

$key = q/rho,{{bf{E}+{{bf{j}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2171.png"
 ALT="$\rho {\bf E} + {\bf j}\times{\bf B}$">|; 

$key = q/displaystyle{{bf{a}cdot({{bf{b}+{{bf{c});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle {\bf a}\cdot({\bf b}+{\bf c})$">|; 

$key = q/{displaymath}{{bf{r}cdot{{bf{b}times{{bf{c}=alpha,{{bf{a}cdot{{bf{b}times{{bf{c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="\begin{displaymath}
{\bf r} \cdot {\bf b} \times{\bf c} = \alpha  {\bf a}\cdot{\bf b} \times{\bf c},
\end{displaymath}">|; 

$key = q/{displaymath}delta({{bf{r})=delta(x),delta(y),delta(z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="\begin{displaymath}
\delta({\bf r}) = \delta(x) \delta(y) \delta(z).
\end{displaymath}">|; 

$key = q/displaystylez,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2656.png"
 ALT="$\displaystyle z,$">|; 

$key = q/{{bf{b}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="${\bf b}(t)$">|; 

$key = q/F,partial^2(|{{bf{r}-{{bf{r'}|^{-1})slashpartialx^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="$F  \partial^2(\vert{\bf r} - {\bf r'}\vert^{-1})/\partial x^2$">|; 

$key = q/{displaymath}F^{munu}=frac{e}{4pi,epsilon_0,c,{r'}^3},(U^muR^nu-U^nuR^mu).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img3133.png"
 ALT="\begin{displaymath}
F^{\mu\nu} = \frac{e}{4\pi \epsilon_0 c {r'}^3} (U^\mu R^\nu
-U^\nu R^\mu).
\end{displaymath}">|; 

$key = q/displaystylephi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="$\displaystyle \phi$">|; 

$key = q/dx'=gamma,(dx-v,dt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2742.png"
 ALT="$dx' = \gamma (dx-v dt)$">|; 

$key = q/{displaymath}nablacdot{{bf{A}=frac{partialA_z}{partialz}simeqfrac{mu_0,l}{4pi}frt(-frac{z}{r^2,c}right)+Oleft(frac{1}{r^2}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2220.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf A} =\frac{\partial A_z}{\partial z} \simeq \...
... \left(-\frac{z}{r^2  c}\right) +O\left(
\frac{1}{r^2}\right)
\end{displaymath}">|; 

$key = q/nablacdot{{bf{E}=0slash0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="$\nabla\cdot
{\bf E} = 0/0$">|; 

$key = q/{displaymath}sigmasimeqfrac{n_e,e^2}{m_e,nu}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2435.png"
 ALT="\begin{displaymath}
\sigma \simeq \frac{n_e e^2}{m_e \nu}.
\end{displaymath}">|; 

$key = q/{displaymath}c=frac{1}{sqrt{epsilon_0mu_0}}=2.998times10^8,{{rm{m},{{rm{s}^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="\begin{displaymath}
c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} = 2.998\times 10^8 {\rm m} {\rm s}^{-1}.
\end{displaymath}">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$z$">|; 

$key = q/dlla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1837.png"
 ALT="$d\ll a$">|; 

$key = q/displaystylenabla^2A_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$\displaystyle \nabla^2 A_z$">|; 

$key = q/rhosim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3334.png"
 ALT="$\rho \sim 1$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="$N$">|; 

$key = q/L_1slashL_2=N_1^{,2}slashN_2^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1935.png"
 ALT="$L_1/L_2 =N_1^{ 2}/N_2^{ 2}$">|; 

$key = q/partialslashpartialt|_{x^i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3239.png"
 ALT="$\partial/\partial t\vert _{x^i}$">|; 

$key = q/F=x,y^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$F=x y^3$">|; 

$key = q/displaystyle-G_{ji}=-E_{ij},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3078.png"
 ALT="$\displaystyle -G_{ji} = -E_{ij},$">|; 

$key = q/displaystylegamma,(T^4-beta,T^1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2887.png"
 ALT="$\displaystyle \gamma (T^4 - \beta  T^1),$">|; 

$key = q/E_{parallel,A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="$E_{\parallel A}$">|; 

$key = q/displaystyleB_{perp,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2498.png"
 ALT="$\displaystyle B_{\perp 1}$">|; 

$key = q/9.4times10^{-31};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="$9.4\times 10^{-31}$">|; 

$key = q/m=1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2633.png"
 ALT="$m=1, 2, \cdots$">|; 

$key = q/partial^2Gslashpartialy^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="$\partial^2 G/\partial y^2$">|; 

$key = q/{displaymath}phi(x,y)=frac{4,phi_0}{pi}sum_{n=1,3,5}frac{exp(-n,x)sin(n,x)}{n}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1641.png"
 ALT="\begin{displaymath}
\phi(x, y) = \frac{4 \phi_0}{\pi}\sum_{n=1, 3, 5}\frac{\exp(-n x)\sin (n x)}{n}.
\end{displaymath}">|; 

$key = q/{displaymath}E^{ij}=E_{ij}=left(array{{ccc}0&E_z&-E_y[0.5ex]-E_z&0&E_x[0.5ex]E_y&-E_x&0array{right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="84" BORDER="0"
 SRC="|."$dir".q|img3057.png"
 ALT="\begin{displaymath}
E^{ij}=E_{ij} = \left(\begin{array}{ccc}
0&amp; E_z &amp; -E_y [0....
...
-E_z &amp; 0 &amp; E_x  [0.5ex]
E_y &amp; -E_x &amp; 0 \end{array} \right),
\end{displaymath}">|; 

$key = q/displaystyle-frac{rho}{epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1402.png"
 ALT="$\displaystyle - \frac{\rho}{\epsilon_0}$">|; 

$key = q/displaystyle0mbox{hspace{2.2cm}otherwise}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="$\displaystyle 0 \mbox{\hspace{2.2cm} otherwise}.$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf l} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}dV'=gammaleft(1+frac{v}{c},costhetaright)dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2996.png"
 ALT="\begin{displaymath}
dV' = \gamma \left(1+\frac{v}{c}  \cos\theta\right) dV.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2,mu_0}int_Vleft[-nablacdot({{bf{A}times{{bf{B})+{{bf{B}cdotnablatimes{{bf{A}right],dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="370" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1998.png"
 ALT="\begin{displaymath}
W = \frac{1}{2 \mu_0} \int_V \left[- \nabla\cdot ({\bf A} \times{\bf B})
+{\bf B}\cdot \nabla \times {\bf A} \right]  dV.
\end{displaymath}">|; 

$key = q/R_mu=(-{{bf{r},c,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2897.png"
 ALT="$R_\mu = (-{\bf r}, c t)$">|; 

$key = q/{displaymath}U_E=frac{epsilon_0,E^2}{2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2104.png"
 ALT="\begin{displaymath}
U_E = \frac{\epsilon_0 E^2}{2},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig31.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="459" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig31.eps}}
\end{figure}">|; 

$key = q/x,y,z,rightarrow-x,-y,-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3010.png"
 ALT="$x,y,z,\rightarrow -x,-y,-z$">|; 

$key = q/{bf{b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\bf b$">|; 

$key = q/nabla';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="$\nabla'$">|; 

$key = q/d^3{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$d^3{\bf r}$">|; 

$key = q/displaystyleintfrac{rho({{bf{r}')}{epsilon_0},delta({{bf{r}-{{bf{r}'),d^3{{bf{r}'=frac{rho({{bf{r})}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$\displaystyle \int \frac{\rho({\bf r}')}{\epsilon_0}  \delta({\bf r} - {\bf r}') 
d^3{\bf r}' = \frac{\rho({\bf r})}{\epsilon_0},$">|; 

$key = q/{{bf{r}_u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3262.png"
 ALT="${\bf r}_u$">|; 

$key = q/A^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2820.png"
 ALT="$A^i$">|; 

$key = q/{displaymath}R=left(frac{E_r}{E_i}right)^2=left(frac{1-alpha,beta}{1+alpha,beta}right)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2544.png"
 ALT="\begin{displaymath}
R = \left(\frac{E_r}{E_i}\right)^2 = \left(\frac{1-\alpha \beta}{1+\alpha \beta}\right)^2,
\end{displaymath}">|; 

$key = q/{displaymath}deltaW=intphi,deltarho_f,d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1754.png"
 ALT="\begin{displaymath}
\delta W = \int \phi  \delta\rho_f  d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}dx'^2+dy'^2+dz'^2-c^2,dt'^2=dx^2+dy^2+dz^2-c^2,dt^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2690.png"
 ALT="\begin{displaymath}
dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2 =dx^2 + dy^2 + dz^2 -c^2  dt^2.
\end{displaymath}">|; 

$key = q/lambda=q'^{,2}slashq^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1527.png"
 ALT="$\lambda=q'^{ 2}/q^2$">|; 

$key = q/-theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$-\theta$">|; 

$key = q/displaystyle{{rm{i},({{bf{k}times{{bf{A})_x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="$\displaystyle {\rm i} ({\bf k} \times {\bf A})_x.$">|; 

$key = q/c=(epsilon_0,mu_0)^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2315.png"
 ALT="$c= (\epsilon_0 \mu_0)^{-1/2}$">|; 

$key = q/displaystyleV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1390.png"
 ALT="$\displaystyle V$">|; 

$key = q/{displaymath}f_nu=epsilon_0left[partial_mu(F^{musigma}F_{nusigma})-F^{musigma},partial_muF_{nusigma}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3191.png"
 ALT="\begin{displaymath}
f_\nu = \epsilon_0
\left[\partial_\mu(F^{\mu\sigma}F_{\nu\sigma})
-F^{\mu\sigma}  \partial_\mu F_{\nu\sigma}\right].
\end{displaymath}">|; 

$key = q/{displaymath}nablatimesnablatimes{{bf{A}equivnabla(nablacdot{{bf{A})-nabla^2{{bfpsilon_0mu_0,frac{partial^2{{bf{A}}{partialt^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="\begin{displaymath}
\nabla\times\nabla\times {\bf A} \equiv
\nabla(\nabla\cdot{\...
...} - \epsilon_0\mu_0 
\frac{\partial^2 {\bf A}}{\partial t^2},
\end{displaymath}">|; 

$key = q/epsilon=n^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2558.png"
 ALT="$\epsilon = n^2$">|; 

$key = q/displaystyle{{it{something},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="$\displaystyle {\it something},$">|; 

$key = q/{displaymath}P=frac{e^2}{6pi,epsilon_0,c^3},dot{u}^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3283.png"
 ALT="\begin{displaymath}
P = \frac{e^2}{6\pi \epsilon_0  c^3}  \dot{u}^2.
\end{displaymath}">|; 

$key = q/q(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2198.png"
 ALT="$q(t)$">|; 

$key = q/B_{23};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3041.png"
 ALT="$B_{23}$">|; 

$key = q/displaystylev_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="$\displaystyle v_z$">|; 

$key = q/n,q,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1944.png"
 ALT="$n q V$">|; 

$key = q/AB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$AB$">|; 

$key = q/epsilon_2ggepsilon_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1727.png"
 ALT="$\epsilon_2\gg \epsilon_1$">|; 

$key = q/{displaymath}nabla^2phi=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="\begin{displaymath}
\nabla^2 \phi = 0,
\end{displaymath}">|; 

$key = q/m_e,c^2=0.511;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3327.png"
 ALT="$m_e  c^2 = 0.511$">|; 

$key = q/d{{bf{S}=dx,dy,hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$d{\bf S} = dx dy \hat{\bf z}$">|; 

$key = q/j_x(y,z),dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$j_x(y,z) dy dz$">|; 

$key = q/{displaymath}frac{partial}{partialx}!left(frac{1}{|{{bf{r}-{{bf{r}'|}right)=-frartialx'}!left(frac{1}{|{{bf{r}-{{bf{r}'|}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial x}\! \left(\frac{1}{\vert{\bf r} - ...
...ial x'} \!\left(\frac{1}{\vert{\bf r} - {\bf r}'\vert}\right),
\end{displaymath}">|; 

$key = q/displaystyleleft(-nabla^2+frac{1}{c^2}frac{partial^2}{partialt^2}right)phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2968.png"
 ALT="$\displaystyle \left(-\nabla^2+\frac{1}{c^2} \frac{\partial^2}{\partial t^2}\right)\phi$">|; 

$key = q/rho=v_perpslash{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$\rho=v_\perp/{\mit\Omega}$">|; 

$key = q/mu_0,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$\mu_0  I$">|; 

$key = q/m=0,1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2617.png"
 ALT="$m=0, 1, 2, \cdots$">|; 

$key = q/{displaymath}v({{bf{r})=intdelta({{bf{r}-{{bf{r}'),v({{bf{r}'),d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="\begin{displaymath}
v({\bf r}) = \int \delta({\bf r} - {\bf r}')  v({\bf r}')  d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{j}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf j} = 0.
\end{displaymath}">|; 

$key = q/displaystylet;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2725.png"
 ALT="$\displaystyle t$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=(E_{perp,A}-E_{perp,B}),A,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="\begin{displaymath}
\oint_S {\bf E} \cdot d{\bf S} = ( E_{\perp A} - E_{\perp B}) A,
\end{displaymath}">|; 

$key = q/{displaymath}phirightarrowphi+c{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="\begin{displaymath}
\phi \rightarrow \phi + c
\end{displaymath}">|; 

$key = q/deltatheta_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\delta\theta_y$">|; 

$key = q/{displaymath}Box{mitPhi}^mu=frac{J^mu}{c,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2975.png"
 ALT="\begin{displaymath}
\Box {\mit \Phi}^\mu = \frac{J^\mu}{c \epsilon_0}.
\end{displaymath}">|; 

$key = q/F^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3072.png"
 ALT="$F^{\mu\nu}$">|; 

$key = q/{mitdiv},({{bf{grad},phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="${\mit div} ({\bf grad} \phi)$">|; 

$key = q/B_{z,1}=B_{z,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2535.png"
 ALT="$B_{z 1} = B_{z 2}$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=int_Vnablacdot{{bf{E},,d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="\begin{displaymath}
\oint_S {\bf E}\cdot d{\bf S} = \int_V \nabla\cdot {\bf E}   d^3{\bf r},
\end{displaymath}">|; 

$key = q/B^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2838.png"
 ALT="$B^i$">|; 

$key = q/displaystyleE_i,{{rm{e}^{,{{rm{i},(k_1,z-omega,t)},hat{{bf{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2450.png"
 ALT="$\displaystyle E_i {\rm e}^{ {\rm i} (k_1 z-\omega t)}
 \hat{\bf x},$">|; 

$key = q/U=T^{44};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3214.png"
 ALT="$U=T^{44}$">|; 

$key = q/epsilon^{alphabetagammadelta}rightarrow-epsilon^{alphabetagammadelta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3013.png"
 ALT="$\epsilon^{\alpha\beta\gamma\delta}
\rightarrow -\epsilon^{\alpha\beta\gamma\delta}$">|; 

$key = q/Z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2074.png"
 ALT="$Z_0$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{left[{{bf{j}({{bf{r}')right]}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int
\frac{\left[{\bf j}({\bf r}')\right]}{\vert{\bf r} - {\bf r}'\vert} d^3{\bf r'}.$">|; 

$key = q/{displaymath}frac{partialU}{partialt}+nablacdot{{bf{u}=-{{bf{E}cdot{{bf{j}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2115.png"
 ALT="\begin{displaymath}
\frac{\partial U}{\partial t} +\nabla\cdot {\bf u} = - {\bf E} \cdot {\bf j}.
\end{displaymath}">|; 

$key = q/{displaymath}P=langleV(t),I(t)rangle,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2014.png"
 ALT="\begin{displaymath}
P = \langle V(t)  I(t) \rangle,
\end{displaymath}">|; 

$key = q/{displaymath}Z=frac{V}{I}={{rm{i},omega,L+frac{1}{{{rm{i},omega,C}+R.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2013.png"
 ALT="\begin{displaymath}
Z = \frac{V}{I} = {\rm i} \omega  L + \frac{1}{{\rm i }  \omega  C} + R.
\end{displaymath}">|; 

$key = q/ineqj;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2788.png"
 ALT="$i\neq j$">|; 

$key = q/{displaymath}epsilon^{alphabetagammadelta}=left{array{{rcl}+1&mbox{hspace{1cm}}&]0&mbox{hspace{1cm}}&mbox{otherwise}array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="559" HEIGHT="84" BORDER="0"
 SRC="|."$dir".q|img2999.png"
 ALT="\begin{displaymath}
\epsilon^{\alpha\beta\gamma\delta} =\left\{
\begin{array}{rc...
...5ex]
0&amp;\mbox{\hspace{1cm}}&amp;\mbox{otherwise}
\end{array}\right.
\end{displaymath}">|; 

$key = q/{displaymath}int_T^inftyI^2R,dt=frac{1}{2},L,I_T^{,2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1954.png"
 ALT="\begin{displaymath}
\int_T^\infty I^2 R  dt = \frac{1}{2}  L  I_T^{ 2},
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{[rho({{bf{r}')]}{|{{bf{r}-{{bf{r}'|},dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2982.png"
 ALT="$\displaystyle \frac{1}{4\pi \epsilon_0} \int
\frac{[\rho({\bf r}')]}{\vert{\bf r}- {\bf r}'\vert} dV',$">|; 

$key = q/g_{44}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2870.png"
 ALT="$g_{44}=1$">|; 

$key = q/displaystylexpm{{rm{i},y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2359.png"
 ALT="$\displaystyle x\pm {\rm i} y,$">|; 

$key = q/F(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2338.png"
 ALT="$F(k)$">|; 

$key = q/P=(infty,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$P=(\infty, 0, 0)$">|; 

$key = q/{displaymath}frac{dsigma}{d{mitOmega}}=left(frac{omega}{omega_0}right)^4,r_e^{,2},sin^2theta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2305.png"
 ALT="\begin{displaymath}
\frac{d\sigma}{d{\mit\Omega}} = \left(\frac{\omega}{\omega_0}\right)^4 r_e^{ 2} \sin^2\theta,
\end{displaymath}">|; 

$key = q/y_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="$y_i$">|; 

$key = q/phi=omega_0,t';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3357.png"
 ALT="$\phi = \omega_0  t'$">|; 

$key = q/{{bf{grad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="${\bf grad}$">|; 

$key = q/displaystyle-epsilon_0mu_0,frac{partialphi}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="$\displaystyle -\epsilon_0 \mu_0  \frac{\partial \phi}{\partial t}.$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig13.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig13.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{partial^2phi}{partialx^2}+frac{partial^2phi}{partialy^2}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1597.png"
 ALT="\begin{displaymath}
\frac{\partial^2\phi}{\partial x^2} + \frac{\partial^2\phi}{\partial y^2} = 0
\end{displaymath}">|; 

$key = q/{displaymath}int_P^Qleft[y^3,dx+x,dyright]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="\begin{displaymath}
\int_P^Q \left[ y^3 dx + x dy\right]
\end{displaymath}">|; 

$key = q/F(z)=z^{3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1592.png"
 ALT="$F(z) = z^{3/2}$">|; 

$key = q/x=y+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$x=y+1$">|; 

$key = q/{displaymath}B_{ij}=-B_{ji}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3017.png"
 ALT="\begin{displaymath}
B_{ij} = -B_{ji}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{j}_t=sigma,({{bf{E}+{{bf{E}'),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1846.png"
 ALT="\begin{displaymath}
{\bf j}_t = \sigma  ({\bf E} + {\bf E}'),
\end{displaymath}">|; 

$key = q/deltaS_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\delta S_i$">|; 

$key = q/displaystyle{{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="$\displaystyle {\bf0}$">|; 

$key = q/{displaymath}P=frac{e^2}{6pi,epsilon_0,m_0^{,2},c^3}left(frac{dE}{dx}right)^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img3324.png"
 ALT="\begin{displaymath}
P= \frac{e^2}{6\pi \epsilon_0  m_0^{ 2}  c^3}\left(\frac{dE}{dx}\right)^2.
\end{displaymath}">|; 

$key = q/{displaymath}sigma=epsilon_0,E_r(r=c)=-epsilon_0,frac{partialphi(r=c)}{partialr}=2,epsilon_0,E_0,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1589.png"
 ALT="\begin{displaymath}
\sigma = \epsilon_0 E_r(r=c) = - \epsilon_0 \frac{\partial\phi(r=c)}{\partial r} =
2 \epsilon_0 E_0 \cos\theta,
\end{displaymath}">|; 

$key = q/{{bf{S}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="${\bf S} = {\bf0}$">|; 

$key = q/{displaymath}E_0+2,E_0,alpha=epsilon,E_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1739.png"
 ALT="\begin{displaymath}
E_0 + 2 E_0 \alpha = \epsilon E_1.
\end{displaymath}">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=oint{{bf{A}cdotd{{bf{l}_1+oint{{bf{A}cdotd{{bf{l}_2+oint{{bf{A}cdotd{{bf{l}_3,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="\begin{displaymath}
\oint {\bf A} \cdot d{\bf l} = \oint {\bf A}\cdot d{\bf l}_1 +
\oint {\bf A}\cdot d{\bf l}_2+\oint {\bf A}\cdot d{\bf l}_3,
\end{displaymath}">|; 

$key = q/{displaymath}dW=frac{4pi}{3,epsilon_0},rho^2,r^4,dr.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="\begin{displaymath}
dW = \frac{4\pi}{3 \epsilon_0}  \rho^2  r^4 dr.
\end{displaymath}">|; 

$key = q/displaystyle-dx^2-dy^2-dz^2+c^2,dt^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2864.png"
 ALT="$\displaystyle -dx^2 -dy^2 -dz^2 +c^2  dt^2$">|; 

$key = q/{displaymath}W=int_0^TVI,dt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1948.png"
 ALT="\begin{displaymath}
W = \int_0^T VI  dt.
\end{displaymath}">|; 

$key = q/{displaymath}r(x^i,{x^i}'(t'),)equivr(x^i,t')=c,(t-t'),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3243.png"
 ALT="\begin{displaymath}
r(x^i, {x^i}'(t') ) \equiv r(x^i, t') = c (t-t'),
\end{displaymath}">|; 

$key = q/{displaymath}Q=frac{1}{c}intJ^4,d^3x=intrho,d^3x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3305.png"
 ALT="\begin{displaymath}
Q = \frac{1}{c} \int J^4 d^3 x= \int \rho d^3 x
\end{displaymath}">|; 

$key = q/n^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2771.png"
 ALT="$n^2$">|; 

$key = q/displaystyle+frac{1}{mu_0}left[nabla(B^2slash2)-(nablacdot{{bf{B}),{{bf{B}-({{bf{B}cdotnabla){{bf{B}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2184.png"
 ALT="$\displaystyle +\frac{1}{\mu_0}\left[\nabla(B^2/2) - (\nabla\cdot {\bf B}) {\bf B} - ({\bf B}\cdot\nabla){\bf B}\right]$">|; 

$key = q/{displaymath}R_{{rm{rad}=frac{2pi}{3,epsilon_0,c}left(frac{l}{lambda}right)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2236.png"
 ALT="\begin{displaymath}
R_{\rm rad} = \frac{2\pi}{3 \epsilon_0  c} \left(\frac{l}{\lambda}\right)^2,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=-nablaphi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="\begin{displaymath}
{\bf E} = - \nabla \phi.
\end{displaymath}">|; 

$key = q/a_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$a_x$">|; 

$key = q/{displaymath}{{bf{j}=sigma,{{bf{E}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2395.png"
 ALT="\begin{displaymath}
{\bf j} = \sigma {\bf E}.
\end{displaymath}">|; 

$key = q/sigma,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$\sigma A$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}=frac{e^2,dot{u}^2}{16pi^2,epsilon_0,c^3}f)tan^2phi,cos^2theta}{[1-(uslashc),costheta]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3369.png"
 ALT="\begin{displaymath}
\frac{d P(t')}{d{\mit\Omega}} = \frac{e^2  \dot{u}^2}{16\pi...
...1-u^2/c^2)\tan^2\phi \cos^2\theta}
{[1-(u/c) \cos\theta]^5}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=int_Vnablacdot{{bf{E},,d^3{{bf{r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="\begin{displaymath}
\oint_S {\bf E} \cdot d{\bf S} = \int_V \nabla\cdot {\bf E}  d^3{\bf r}
\end{displaymath}">|; 

$key = q/{displaymath}m_e,frac{d^2z}{dt^2}=-m_e,omega_0^{,2},z-e,E_0,sin(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2298.png"
 ALT="\begin{displaymath}
m_e \frac{d^2 z}{dt^2} = - m_e \omega_0^{ 2} z - e E_0 \sin(\omega t).
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="\begin{displaymath}
\nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}
\end{displaymath}">|; 

$key = q/{{rm{TM}_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2635.png"
 ALT="${\rm TM}_{11}$">|; 

$key = q/{displaymath}deltaW={{bf{f}cdotdelta{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="\begin{displaymath}
\delta W = {\bf f}\cdot \delta {\bf r}.
\end{displaymath}">|; 

$key = q/T^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2878.png"
 ALT="$T^\mu$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig21.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig21.eps}}
\end{figure}">|; 

$key = q/displaystyleint_a^bE_r,dr=frac{q}{2pi,epsilon_0}int_a^bfrac{dr}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1392.png"
 ALT="$\displaystyle \int_a^b E_r dr = \frac{q}{2\pi  \epsilon_0} \int_a^b \frac{dr}{r},$">|; 

$key = q/{displaymath}nablatimes{{bf{F}=nablatimesnablatimes{{bf{W}=nabla(nablacdot{{bf{W})-nabla^2{{bf{W}=-nabla^2{{bf{W}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="445" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="\begin{displaymath}
\nabla\times{\bf F} = \nabla\times\nabla\times{\bf W}= \nabla(\nabla\cdot{\bf W})
- \nabla^2{\bf W} = -\nabla^2 {\bf W}.
\end{displaymath}">|; 

$key = q/displaystyleI_0,exp({{rm{i},omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2010.png"
 ALT="$\displaystyle I_0  \exp({\rm i} \omega  t),$">|; 

$key = q/gamma(u)gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3144.png"
 ALT="$\gamma(u)\gg 1$">|; 

$key = q/[nablacdot{{bf{j}]=-[partial{{bf{j}slashpartialt]cdot{{bf{R}slashcR+O(1slashR^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="$[\nabla\cdot {\bf j} ] = -[\partial {\bf j}/\partial t]\cdot {\bf R}/c R + O(1/R^2)$">|; 

$key = q/{displaymath}P=frac{1}{2},|V_0|,|I_0|costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2020.png"
 ALT="\begin{displaymath}
P = \frac{1}{2}  \vert V_0\vert  \vert I_0\vert \cos\theta,
\end{displaymath}">|; 

$key = q/Rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2088.png"
 ALT="$R\rightarrow \infty$">|; 

$key = q/{displaymath}int!int_{S_1}{{bf{v}cdotd{{bf{S}=intint_{S_2}{{bf{v}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="\begin{displaymath}
\int\!\int_{S_1} {\bf v}\cdot d{\bf S} = \int\int_{S_2} {\bf v}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/{displaymath}{calE}(Q)=q,phi(Q).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="\begin{displaymath}
{\cal E} (Q)= q  \phi(Q).
\end{displaymath}">|; 

$key = q/{displaymath}phirightarrow0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1487.png"
 ALT="\begin{displaymath}
\phi\rightarrow 0
\end{displaymath}">|; 

$key = q/{{bf{A}({{bf{r},t)=A_z({{bf{r},t),hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2209.png"
 ALT="${\bf A}({\bf r}, t) = A_z({\bf r}, t)  \hat{\bf z}$">|; 

$key = q/{displaymath}nabla!cdot!{{bf{E}=frac{rho}{epsilon_0}=frac{rho_f+rho_b}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1677.png"
 ALT="\begin{displaymath}
\nabla\!\cdot\!{\bf E} = \frac{\rho}{\epsilon_0} =
\frac{\rho_f + \rho_b}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/displaystylephi+c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$\displaystyle \phi +c,$">|; 

$key = q/{displaymath}P={{bf{j}cdot{{bf{E}=eta,j^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="\begin{displaymath}
P = {\bf j} \cdot {\bf E} = \eta  j^2,
\end{displaymath}">|; 

$key = q/{{bf{B}=mu,{{bf{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1816.png"
 ALT="${\bf B} = \mu {\bf H}$">|; 

$key = q/dF=y^3,dx+3,x,y^2,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$dF= y^3 dx + 3 x  y^2 dy$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig1rel.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img3295.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig1rel.eps}}
\end{figure}">|; 

$key = q/rho({{bf{r}'),d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="$\rho({\bf r}') d^3{\bf r}'$">|; 

$key = q/int_{S_1}{{bf{j}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$\int_{S_1} {\bf j}
\cdot d{\bf S} $">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=left(frac{partialA_z}{partialy}-frac{partialA_y}{partialz}right)dS_x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="\begin{displaymath}
\oint {\bf A} \cdot d{\bf l} = \left(\frac{\partial A_z}{\partial y}-
\frac{\partial A_y}{\partial z}\right) dS_x
\end{displaymath}">|; 

$key = q/{displaymath}B^i=frac{1}{2},epsilon^{ijk}B_{jk}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3018.png"
 ALT="\begin{displaymath}
B^i = \frac{1}{2}  \epsilon^{ijk} B_{jk}.
\end{displaymath}">|; 

$key = q/{displaymath}dx^{i'}=frac{partialx^{i'}}{partialx^i},dx^i=dx^i,p_i^{i'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2801.png"
 ALT="\begin{displaymath}
dx^{i'} = \frac{\partial x^{i'}}{\partial x^i}  dx^i = dx^i  p_i^{i'}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}equiv(a_x,,a_y,,a_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
{\bf a} \equiv (a_x,  a_y,  a_z).
\end{displaymath}">|; 

$key = q/{{bf{a}={{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="${\bf a} = {\bf b}$">|; 

$key = q/displaystyleT^{3'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2884.png"
 ALT="$\displaystyle T^{3'}$">|; 

$key = q/{displaymath}nablatimes{{bf{B}_3={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1459.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B}_3={\bf0}
\end{displaymath}">|; 

$key = q/r^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2001.png"
 ALT="$r^{-2}$">|; 

$key = q/10^{-9};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$10^{-9}$">|; 

$key = q/omega=1slashsqrt{L,C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2030.png"
 ALT="$\omega = 1/\sqrt{L C}$">|; 

$key = q/P_1,P_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2826.png"
 ALT="$P_1, P_2,$">|; 

$key = q/A^{ijcdotsk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2793.png"
 ALT="$A^{ij\cdots k}$">|; 

$key = q/displaystylefrac{dx}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2730.png"
 ALT="$\displaystyle \frac{dx}{dt},$">|; 

$key = q/T({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$T({\bf r})$">|; 

$key = q/{displaymath}frac{dI}{dt}+frac{R}{L},I=frac{V}{L}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1896.png"
 ALT="\begin{displaymath}
\frac{dI}{dt}+ \frac{R}{L} I= \frac{V}{L}.
\end{displaymath}">|; 

$key = q/{displaymath}sigmasimeqfrac{{{rm{i},n_e,e^2}{m_e,omega}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2433.png"
 ALT="\begin{displaymath}
\sigma \simeq \frac{{\rm i} n_e e^2}{m_e \omega}.
\end{displaymath}">|; 

$key = q/{displaymath}E_x={{rm{i}left(omega,frac{partialB_z}{partialy}+k,frac{partialE_z}lx}right)left(frac{omega^2}{c^2}-k^2right)^{-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2589.png"
 ALT="\begin{displaymath}
E_x = {\rm i}\left(\omega \frac{\partial B_z}{\partial y} +...
...{\partial x}\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1},
\end{displaymath}">|; 

$key = q/U=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1584.png"
 ALT="$U=0$">|; 

$key = q/{displaymath}y'=A,y,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2701.png"
 ALT="\begin{displaymath}
y' = A y,
\end{displaymath}">|; 

$key = q/E_r=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1389.png"
 ALT="$E_r=0$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}=a_x,b_x+a_y,b_y+a_z,b_z{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="\begin{displaymath}
{\bf a}\cdot{\bf b} = a_x  b_x + a_y  b_y + a_z  b_z
\end{displaymath}">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$R$">|; 

$key = q/r^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2221.png"
 ALT="$r^{-1}$">|; 

$key = q/B_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2606.png"
 ALT="$B_z=0$">|; 

$key = q/{displaymath}g_{ij},A^i,B^j=A_i,B^i=A^i,B_i=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2846.png"
 ALT="\begin{displaymath}
g_{ij}  A^i  B^j = A_i  B^i = A^i  B_i = 0.
\end{displaymath}">|; 

$key = q/{displaymath}V(x,t)-V(x+deltax,t)=L,deltax,frac{partialI(x,t)}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2043.png"
 ALT="\begin{displaymath}
V(x, t) -V(x+\delta x, t) = L \delta x \frac{\partial I(x, t)}{\partial t},
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0  {\bf j},
\end{displaymath}">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$W$">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}int_{z>0}E^2,dV=frac{epsilon_0}{2}int_{z>0}E_{{rm{analogue}^2,dV=frac{1}{2},W_{{rm{analogue},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1514.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \int_{z&gt;0} E^2 dV=
\frac{\epsilon_...
...&gt;0} E_{\rm analogue}^2  dV =
\frac{1}{2}  W_{\rm analogue},
\end{displaymath}">|; 

$key = q/{displaymath}(E_i+E_r),costheta_i=E_t,costheta_t.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2555.png"
 ALT="\begin{displaymath}
(E_i+E_r) \cos\theta_i = E_t \cos\theta_t.
\end{displaymath}">|; 

$key = q/{displaymath}phi_m(r,theta)=-(B_0slashmu_0),r,costheta+(B_0slashmu_0),alpha,frac{a^3,costheta}{r^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1822.png"
 ALT="\begin{displaymath}
\phi_m(r,\theta) = - (B_0/\mu_0) r \cos\theta + (B_0/\mu_0) \alpha  \frac{a^3 \cos\theta}{r^2}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}simeq-frac{omega,l,I_0}{4pi,epsilon_0,c^2},sintheta,frac{singa(t-rslashc)]}{r},hat{mbox{{boldmath{{theta{}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2224.png"
 ALT="\begin{displaymath}
{\bf E} \simeq - \frac{\omega  l  I_0}{4\pi  \epsilon_0 \...
...rac{\sin[\omega (t-r/c)]}{r}  \hat{\mbox{\boldmath$\theta$}},
\end{displaymath}">|; 

$key = q/E_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2368.png"
 ALT="$E_\pm$">|; 

$key = q/{displaymath}F_{munu}=leftlgrouparray{{cccc}0&-c,B_z&+c,B_y&-E_x[0.5ex]+c,B_z&0&&0&-E_z[0.5ex]+E_x&+E_y&+E_z&0array{rightrgroup.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="111" BORDER="0"
 SRC="|."$dir".q|img3038.png"
 ALT="\begin{displaymath}
F_{\mu\nu} = \left\lgroup \begin{array}{cccc}
0 &amp; -c B_z &amp; ...
...-E_z [0.5ex]
+E_x &amp; +E_y &amp;+E_z &amp; 0\end{array}\right
\rgroup.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3125.png"
 ALT="$\displaystyle {\bf B}'$">|; 

$key = q/{{bf{j}=e,n,{{bf{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3183.png"
 ALT="${\bf j} = e  n  {\bf u}$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{rho({{bf{r'},t')}{4pi,epsilon_0}frac{delta(t-t'-|{{bf{r}-{{bf{r'}|slashc)}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{\rho({\bf r'}, t')}{4\pi  \epsilon...
...vert{\bf r} - {\bf r'}\vert/c)}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{displaymath}|I_0|=frac{|V_0|}{|Z|}=frac{|V_0|}{sqrt{(omega,L-1slashomega,C)^2+R^2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img2029.png"
 ALT="\begin{displaymath}
\vert I_0\vert = \frac{\vert V_0\vert}{\vert Z\vert}= \frac{\vert V_0\vert}{\sqrt{(\omega  L-1/\omega  C)^2 + R^2}}.
\end{displaymath}">|; 

$key = q/theta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="$\theta=0$">|; 

$key = q/displaystyleF_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3036.png"
 ALT="$\displaystyle F_{ij}$">|; 

$key = q/displaystylep_{i'}^i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2785.png"
 ALT="$\displaystyle p_{i'}^i.$">|; 

$key = q/{displaymath}dt=-frac{dr}{c}=-frac{dx}{c},costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2994.png"
 ALT="\begin{displaymath}
dt = -\frac{dr}{c} = -\frac{dx}{c} \cos\theta.
\end{displaymath}">|; 

$key = q/>10^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$&gt;10^1$">|; 

$key = q/{displaymath}F_{munu}=partial_mu{mitPhi}_nu-partial_nu{mitPhi}_mu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3030.png"
 ALT="\begin{displaymath}
F_{\mu\nu} = \partial_\mu {\mit \Phi}_\nu -\partial_\nu {\mit \Phi}_\mu.
\end{displaymath}">|; 

$key = q/g_x,frightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$g_x f \rightarrow 0$">|; 

$key = q/{displaymath}U=frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0}=frac{epsilon_0,E^2}{2}+frac{E^2}{2,mu_0,c^2}=epsilon_0,E^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2130.png"
 ALT="\begin{displaymath}
U = \frac{\epsilon_0 E^2}{2} + \frac{B^2}{2 \mu_0} = \frac...
...on_0 E^2}{2}
+ \frac{E^2}{2 \mu_0  c^2} = \epsilon_0  E^2,
\end{displaymath}">|; 

$key = q/{displaymath}m_e,frac{d{{bf{v}}{dt}+m_e,nu,{{bf{v}=-e,{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2424.png"
 ALT="\begin{displaymath}
m_e \frac{d{\bf v}}{dt} + m_e \nu {\bf v} = -e {\bf E},
\end{displaymath}">|; 

$key = q/{displaymath}Z_0=60,frac{ln(bslasha)}{sqrt{epsilon}},,{{rm{ohms}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2073.png"
 ALT="\begin{displaymath}
Z_ 0 = 60 \frac{\ln(b/a)}{\sqrt{\epsilon}}  {\rm ohms}.
\end{displaymath}">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="$i$">|; 

$key = q/displaystylefrac{Q_i}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1430.png"
 ALT="$\displaystyle \frac{Q_i}{\epsilon_0},$">|; 

$key = q/{mitDelta}k=(1slash2),(omega_p^{,2}slashomega^2),{mitOmega}slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2380.png"
 ALT="${\mit\Delta} k = (1/2) (\omega_p^{ 2}/\omega^2) {\mit \Omega}/c$">|; 

$key = q/{displaymath}frac{4pi,epsilon_0}{e},{{bf{E}=frac{nablas}{s^2}-frac{partial}{partialt}frac{{bf{u}{s,c^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3251.png"
 ALT="\begin{displaymath}
\frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{\nabla s}{s^2} - \frac{\partial}
{\partial t} \frac{\bf u}{s  c^2},
\end{displaymath}">|; 

$key = q/dx^muslashds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2941.png"
 ALT="$dx^\mu/ds$">|; 

$key = q/{{bf{r}={{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="${\bf r} = {\bf r}'$">|; 

$key = q/{displaymath}nabla^2u=v{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="\begin{displaymath}
\nabla^2 u = v
\end{displaymath}">|; 

$key = q/{displaymath}d=sqrt{frac{2}{mu_0,sigma,omega}}simeqfrac{6}{sqrt{omega({{rm{Hz})}},{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img2415.png"
 ALT="\begin{displaymath}
d = \sqrt{\frac{2}{\mu_0 \sigma \omega}} \simeq \frac{6}{\sqrt{\omega({\rm Hz})}} {\rm cm}.
\end{displaymath}">|; 

$key = q/displaystylek_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2612.png"
 ALT="$\displaystyle k_x$">|; 

$key = q/{displaymath}intB_3^{,2},dV=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1468.png"
 ALT="\begin{displaymath}
\int B_3^{ 2} dV = 0.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{W}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$\nabla\cdot {\bf W} = 0$">|; 

$key = q/{displaymath}P=frac{e^2}{6pi,epsilon_0,c^3},gamma^6,left[dot{{bf{u}^2-frac{({{bf{u}timesdot{{bf{u})^2}{c^2}right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3320.png"
 ALT="\begin{displaymath}
P= \frac{e^2}{6\pi \epsilon_0  c^3}  \gamma^6  \left[ \dot{\bf u}^2 -
\frac{({\bf u}\times\dot{\bf u})^2}{c^2}\right].
\end{displaymath}">|; 

$key = q/{{bf{a},&,{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="${\bf a} \&amp; {\bf b}$">|; 

$key = q/displaystylefrac{dz}{dt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2734.png"
 ALT="$\displaystyle \frac{dz}{dt}.$">|; 

$key = q/{displaymath}frac{1}{4},G_{munu}F^{munu}=c,{{bf{E}!cdot!{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3102.png"
 ALT="\begin{displaymath}
\frac{1}{4}  G_{\mu\nu} F^{\mu\nu} = c {\bf E}\!\cdot \! {\bf B}.
\end{displaymath}">|; 

$key = q/56;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2039.png"
 ALT="$56$">|; 

$key = q/displaystyle0mbox{hspace{0.5cm}as~~~{|{{bf{r}|rightarrowinfty{},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="$\displaystyle 0\mbox{\hspace{0.5cm}as&nbsp;&nbsp;&nbsp;$\vert{\bf r}\vert \rightarrow \infty$},$">|; 

$key = q/{displaymath}omega^2=frac{k^2,c^2}{epsilon}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2332.png"
 ALT="\begin{displaymath}
\omega^2 = \frac{k^2 c^2}{\epsilon}.
\end{displaymath}">|; 

$key = q/underline{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\underline{a}$">|; 

$key = q/beta=uslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3387.png"
 ALT="$\beta=u/c$">|; 

$key = q/displaystylenablaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="$\displaystyle \nabla\phi$">|; 

$key = q/{displaymath}phi_{{rm{analogue}(x,y,z)=frac{1}{4pi,epsilon_0}left{frac{q}{sqrt{x+(z-d)^2}}-frac{q}{sqrt{x^2+y^2+(z+d)^2}}right}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="586" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img1489.png"
 ALT="\begin{displaymath}
\phi_{\rm analogue} (x, y, z) = \frac{1}{4\pi \epsilon_0}
\...
...{x^2+y^2+(z-d)^2}}- \frac{q}{\sqrt{x^2+y^2+
(z+d)^2}}\right\}.
\end{displaymath}">|; 

$key = q/displaystylegammaleft(c,A_1'+frac{u}{c},phi'right)=frac{gamma,u,e}{4pi,epsilon_0,c,r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3110.png"
 ALT="$\displaystyle \gamma\left(c A_1' + \frac{u}{c}  \phi'\right)=
\frac{\gamma  u e}{4\pi \epsilon_0  c  r'},$">|; 

$key = q/phi_{{rm{analogue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1492.png"
 ALT="$\phi_{\rm analogue}$">|; 

$key = q/deltaz=deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1550.png"
 ALT="$\delta z = \delta x$">|; 

$key = q/E^irightarrow-c,B^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3074.png"
 ALT="$E^i\rightarrow -c B^i$">|; 

$key = q/dV=dx,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$dV = dx  dy  dz$">|; 

$key = q/{{bf{B}_3={{bf{B}_1-{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1458.png"
 ALT="${\bf B}_3={\bf B}_1-{\bf B}_2$">|; 

$key = q/displaystyle{{bf{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3358.png"
 ALT="$\displaystyle {\bf u}$">|; 

$key = q/I_{0,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1982.png"
 ALT="$I_{0 i}$">|; 

$key = q/displaystylelangle{{bf{g}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2153.png"
 ALT="$\displaystyle \langle {\bf g} \rangle$">|; 

$key = q/{displaymath}P_{{rm{in}=langleVIrangle=frac{V_0^{,2}}{2,(R_{{rm{rad}+R_{{rm{load})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2247.png"
 ALT="\begin{displaymath}
P_{\rm in} = \langle VI\rangle = \frac{V_0^{ 2}}{2 (R_{\rm rad} + R_{\rm load})}.
\end{displaymath}">|; 

$key = q/{displaymath}oint{{bf{B}cdotd{{bf{l}=epsilon_0mu_0,frac{partial}{partialt}!int{{bf{E}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="\begin{displaymath}
\oint {\bf B} \cdot d{\bf l} = \epsilon_0 \mu_0  \frac{\partial}{\partial t}\!
\int {\bf E} \cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/int{mitdiv},{{bf{A},,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$\int {\mit div} {\bf A}  dV$">|; 

$key = q/displaystyleBox^2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="$\displaystyle \Box^2 \phi$">|; 

$key = q/{displaymath}omega_{mn}=c,pi,sqrt{frac{n^2}{a^2}+frac{m^2}{b^2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2623.png"
 ALT="\begin{displaymath}
\omega_{mn} = c \pi \sqrt{\frac{n^2}{a^2} + \frac{m^2}{b^2}}.
\end{displaymath}">|; 

$key = q/Deltat>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2765.png"
 ALT="$\Delta t&gt;0$">|; 

$key = q/epsilon^{alphabetagammadelta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3003.png"
 ALT="$\epsilon^{\alpha\beta\gamma\delta}$">|; 

$key = q/{displaymath}U^mu=frac{dx^mu}{dtau}=frac{dx^mu}{dt}frac{dt}{dtau}=gamma(u),({{bf{u},c),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2945.png"
 ALT="\begin{displaymath}
U^\mu = \frac{dx^\mu}{d\tau} = \frac{dx^\mu}{dt}\frac{dt}{d\tau}
= \gamma(u)  ({\bf u}, c),
\end{displaymath}">|; 

$key = q/2,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="$2 a$">|; 

$key = q/{displaymath}{{bf{grad},phi=left(frac{partialphi}{partialx},,frac{partialphi}{partialy},,frac{partialphi}{partialz}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="\begin{displaymath}
{\bf grad} \phi = \left(\frac{\partial \phi}{\partial x}, ...
...\phi}
{\partial y},  \frac{\partial \phi}{\partial z}\right),
\end{displaymath}">|; 

$key = q/phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1398.png"
 ALT="$\phi_1$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intleft(nabla(R^{-1})times[{{bf{j}]+frac{nablat_rtimes[partial{{bf{j}slashpartialt]}{R}right),dV';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \left(
\nabla(R^{-1}) \times [{\bf j}] + \frac{\nabla t_r\times [\partial {\bf j}/\partial t]}{R}
\right) dV'$">|; 

$key = q/{displaymath}{{bf{a}+{{bf{b}equiv(a_x+b_x,,a_y+b_y,,a_z+b_z){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="\begin{displaymath}
{\bf a}+ {\bf b} \equiv (a_x+b_x, a_y+b_y,  a_z+b_z)
\end{displaymath}">|; 

$key = q/s_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2374.png"
 ALT="$s_-$">|; 

$key = q/x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$x=0$">|; 

$key = q/{displaymath}int{{bf{g}cdotnablaf,d^3{{bf{r}=-intf,nablacdot{{bf{g},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="\begin{displaymath}
\int {\bf g}\cdot\nabla f d^3{\bf r} = - \int f \nabla\cdot {\bf g} d^3{\bf r},
\end{displaymath}">|; 

$key = q/displaystylenablatimes{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1455.png"
 ALT="$\displaystyle \nabla\times{\bf B}_2$">|; 

$key = q/displaystylenablatimes{{bf{A}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="$\displaystyle \nabla\times{\bf A}.$">|; 

$key = q/{displaymath}{{bf{r}=alpha,{{bf{a}+beta,{{bf{b}+gamma,{{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="\begin{displaymath}
{\bf r} = \alpha  {\bf a} + \beta {\bf b} + \gamma  {\bf c}.
\end{displaymath}">|; 

$key = q/{displaymath}P=frac{1}{4}(V,I^ast+V^ast,I)=frac{1}{2},{{rm{Re}(V,I^ast).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2026.png"
 ALT="\begin{displaymath}
P = \frac{1}{4} ( V  I^\ast + V^\ast  I) = \frac{1}{2}  {\rm Re}(V  I^\ast).
\end{displaymath}">|; 

$key = q/{displaymath}alpha=frac{costheta_t}{costheta_i},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2539.png"
 ALT="\begin{displaymath}
\alpha =\frac{\cos\theta_t}{\cos\theta_i},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{v}=mbox{{boldmath{{omega{}times({{bf{r}-{{bf{r}_0)+mbox{{boldmath{{omega{}times{{bf{r}_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="\begin{displaymath}
{\bf v} = \mbox{\boldmath$\omega$}\times ({\bf r}-{\bf r}_0) +
\mbox{\boldmath$\omega$}\times {\bf r}_0.
\end{displaymath}">|; 

$key = q/displaystylexcostheta+ysintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle x\cos\theta + y\sin \theta,$">|; 

$key = q/{{rm{TE}_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2627.png"
 ALT="${\rm TE}_{10}$">|; 

$key = q/displaystyle(a_x,costheta+a_y,sintheta),(b_x,costheta+b_y,sintheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle (a_x  \cos\theta+a_y \sin\theta) (b_x \cos\theta + b_y \sin\theta)$">|; 

$key = q/x=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1474.png"
 ALT="$x=d$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j}_t+mu_0nablatimes{{bf{M}+mu_0frac{partial{{bf{D}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1779.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0 {\bf j}_t +\mu_0\nabla\times{\bf M}
+ \mu_0\frac{\partial{\bf D}}{\partial t},
\end{displaymath}">|; 

$key = q/exp(-{{rm{i},omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2355.png"
 ALT="$\exp(-{\rm i} \omega t)$">|; 

$key = q/displaystyleV_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1955.png"
 ALT="$\displaystyle V_1$">|; 

$key = q/{{bf{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2319.png"
 ALT="${\bf p}$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig15.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig15.eps}}
\end{figure}">|; 

$key = q/dot{u}=u^2slashrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3331.png"
 ALT="$\dot{u} = u^2/\rho$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig46.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="341" BORDER="0"
 SRC="|."$dir".q|img1904.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig46.eps}}
\end{figure}">|; 

$key = q/displaystyleG_{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3075.png"
 ALT="$\displaystyle G_{i4}$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=frac{1}{epsilon_0}int_Vrho,dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="\begin{displaymath}
\oint_S {\bf E} \cdot d{\bf S} = \frac{1}{\epsilon_0} \int_V \rho  dV,
\end{displaymath}">|; 

$key = q/g^i=T^{4i}slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3220.png"
 ALT="$g^i = T^{4i}/c$">|; 

$key = q/{displaymath}|{{bf{u}|=c,U=epsilon_0,c,E^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2131.png"
 ALT="\begin{displaymath}
\vert{\bf u}\vert = c U = \epsilon_0  c  E^2,
\end{displaymath}">|; 

$key = q/{displaymath}v_p=frac{omega}{k}=frac{c}{sqrt{1-omega_{mn}^{,2}slashomega^2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2629.png"
 ALT="\begin{displaymath}
v_p = \frac{\omega}{k} = \frac{c}{\sqrt{1-\omega_{mn}^{ 2}/\omega^2}},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=eta,{{bf{j}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="\begin{displaymath}
{\bf E} = \eta  {\bf j}.
\end{displaymath}">|; 

$key = q/displaystylepartial_muG^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3091.png"
 ALT="$\displaystyle \partial_\mu G^{\mu\nu}$">|; 

$key = q/E_{{rm{sheet};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="$E_{\rm
sheet}$">|; 

$key = q/{displaymath}frac{partialphi}{partialz}=frac{q}{4pi,epsilon_0}left{frac{-(z-d)}{+frac{(z+d)}{[x^2+y^2+(z+d)^2]^{3slash2}}right},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="514" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1499.png"
 ALT="\begin{displaymath}
\frac{\partial\phi}{\partial z} = \frac{q}{4\pi  \epsilon_0...
...-d)^2]^{3/2}} +
\frac{(z+d)}{[x^2+y^2+(z+d)^2]^{3/2}}\right\},
\end{displaymath}">|; 

$key = q/{displaymath}F(z)=z^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1541.png"
 ALT="\begin{displaymath}
F(z) = z^2,
\end{displaymath}">|; 

$key = q/{{bf{a}times({{bf{b}times{{bf{c});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="${\bf a}\times({\bf b} \times {\bf c})$">|; 

$key = q/sigma_T,l,n_esim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2293.png"
 ALT="$\sigma_T l  n_e\sim 1$">|; 

$key = q/{displaymath}dx^2+dy^2+dz^2-c^2,dt^2=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2665.png"
 ALT="\begin{displaymath}
dx^2 + dy^2 + dz^2 -c^2  dt^2 = 0
\end{displaymath}">|; 

$key = q/B_r=B_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$B_r=B_z = 0$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$F$">|; 

$key = q/{displaymath}E_r(r)=frac{Q}{4pi,epsilon_0}frac{r}{a^3}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="\begin{displaymath}
E_r(r) = \frac{Q}{4\pi  \epsilon_0} \frac{r}{a^3}
\end{displaymath}">|; 

$key = q/displaystyleF_z({{bf{k}cdot{{bf{r}-k,c,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$\displaystyle F_z ({\bf k}\cdot{\bf r} - k c t),$">|; 

$key = q/K=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2084.png"
 ALT="$K= 0$">|; 

$key = q/displaystylex';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle x'$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig16.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig16.eps}}
\end{figure}">|; 

$key = q/{{bf{r}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="${\bf r}_1$">|; 

$key = q/u=a,omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3362.png"
 ALT="$u=a \omega_0$">|; 

$key = q/{displaymath}int{{bf{E}!cdot!(nablatimes{{bf{H}),d^3{{bf{r}=-int{{bf{H}!cdot!fra3{{bf{r}-int({{bf{E}times{{bf{H})!cdot!d{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1851.png"
 ALT="\begin{displaymath}
\int{\bf E}\!\cdot\!(\nabla\times{\bf H}) d^3{\bf r}
= -\i...
... t} d^3{\bf r}
- \int({\bf E}\times{\bf H})\!\cdot\!d{\bf S}.
\end{displaymath}">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{S}=left(frac{partialA_x}{partialx}+frac{partiay}{partialy}+frac{partialA_z}{partialz}right)dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf S} = \left(\frac{\partial A_x}{\par...
...ial A_y}{\partial y}+\frac{\partial A_z}{\partial z}\right)dV.
\end{displaymath}">|; 

$key = q/{displaymath}Deltatsimfrac{b}{gamma,c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3145.png"
 ALT="\begin{displaymath}
\Delta t \sim \frac{b}{\gamma  c},
\end{displaymath}">|; 

$key = q/{displaymath}B_0=frac{E_0}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="\begin{displaymath}
B_0= \frac{E_0}{c}.
\end{displaymath}">|; 

$key = q/{displaymath}deltaW=-intnablaphi!cdot!delta{{bf{D},d^3{{bf{r}=int{{bf{E}!cdot!delta{{bf{D},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1759.png"
 ALT="\begin{displaymath}
\delta W = -\int\nabla\phi \!\cdot\!\delta{\bf D} d^3{\bf r}
= \int {\bf E}\!\cdot\! \delta {\bf D} d^3{\bf r}.
\end{displaymath}">|; 

$key = q/phi(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2641.png"
 ALT="$\phi(x,y)$">|; 

$key = q/d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="$d$">|; 

$key = q/F(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="$F(\phi)$">|; 

$key = q/{displaymath}nabla^2{{bf{A}=nabla,(nablacdot{{bf{A})-nablatimesnablatimes{{bf{A}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="\begin{displaymath}
\nabla^2{\bf A} = \nabla (\nabla\cdot{\bf A})- \nabla\times\nabla\times{\bf A}
\end{displaymath}">|; 

$key = q/{{bf{a}=(1slashsqrt{2},,-1slashsqrt{2},,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="${\bf a} = (1/\sqrt{2},  -1/\sqrt{2},  0)$">|; 

$key = q/displaystyleB_{parallel,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2464.png"
 ALT="$\displaystyle B_{\parallel 2}.$">|; 

$key = q/nablatimes{{bf{E}neq{{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="$\nabla\times{\bf E} \neq {\bf0}$">|; 

$key = q/{displaymath}(nablatimes{{bf{A})_z=frac{1}{r}frac{partial(rA_theta)}{partialr}-frac{1}{r}frac{partialA_r}{partialtheta}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf A})_z = \frac{1}{r}\frac{\partial (r A_\theta)}{\partial r}-\frac{1}{r}\frac{\partial A_r}{\partial \theta}
\end{displaymath}">|; 

$key = q/mu=BslashH;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1801.png"
 ALT="$\mu = B/H$">|; 

$key = q/blla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1381.png"
 ALT="$b\ll a$">|; 

$key = q/crightarrowcslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2316.png"
 ALT="$c\rightarrow c/n$">|; 

$key = q/{displaymath}phi({{bf{r})rightarrow0~~~{{rm{as}~~~|{{bf{r}|rightarrowinfty,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="\begin{displaymath}
\phi({\bf r}) \rightarrow 0&nbsp;&nbsp;&nbsp;{\rm as}&nbsp;&nbsp;&nbsp;\vert{\bf r}\vert \rightarrow \infty,
\end{displaymath}">|; 

$key = q/{{bf{a},&,{{bf{b}=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="${\bf a} \&amp; {\bf b} = 1/2$">|; 

$key = q/dq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="$dq$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{1}{4pi,epsilon_0}intintfrac{delta(t-t'-|{{bf{r}bf{r'},t')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',dt',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="445" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) =\frac{1}{4\pi  \epsilon_0} \int\int\frac{...
...\bf r'}, t')}{\vert{\bf r} - {\bf r}'\vert} d^3{\bf r}' dt',
\end{displaymath}">|; 

$key = q/{displaymath}f^nu=-partial_muT^{munu},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3204.png"
 ALT="\begin{displaymath}
f^\nu =-\partial_\mu T^{\mu\nu},
\end{displaymath}">|; 

$key = q/sigma=pmQslashA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="$\sigma = \pm Q/A$">|; 

$key = q/q(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$q(r)$">|; 

$key = q/R_{{rm{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2244.png"
 ALT="$R_{\rm rad}$">|; 

$key = q/displaystylem_e,omega^2,y=e,(E_y+{{rm{i},omega,B_0,x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2357.png"
 ALT="$\displaystyle m_e \omega^2 y = e (E_y+{\rm i} \omega B_0 x).$">|; 

$key = q/l,d_1+m,d_2+n,d_3=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2693.png"
 ALT="$l d_1 +m  d_2 + n d_3=0$">|; 

$key = q/{displaymath}B_theta=frac{mu_0,I}{2pi,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2067.png"
 ALT="\begin{displaymath}
B_\theta = \frac{\mu_0  I}{2\pi  r}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E}_0,{{rm{e}^{,{{rm{i},({{bf{k}cdot{{bf{r}-omega,t)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="$\displaystyle {\bf E}_0  {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r} - \omega  t)},$">|; 

$key = q/{displaymath}B_c=B_g.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1840.png"
 ALT="\begin{displaymath}
B_c = B_g.
\end{displaymath}">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$c$">|; 

$key = q/{displaymath}intf({{bf{r}),delta({{bf{r}-{{bf{r}'),d^3{{bf{r}=f({{bf{r}').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="\begin{displaymath}
\int f({\bf r}) \delta({\bf r}- {\bf r}') d^3{\bf r}= f({\bf r}').
\end{displaymath}">|; 

$key = q/{displaymath}d=frac{1}{k_r}=sqrt{frac{2}{mu_0,sigma,omega}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2408.png"
 ALT="\begin{displaymath}
d = \frac{1}{k_r} = \sqrt{\frac{2}{\mu_0 \sigma \omega}}.
\end{displaymath}">|; 

$key = q/{displaymath}m,frac{d{{bf{v}}{dr}=q,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="\begin{displaymath}
m \frac{d{\bf v}}{dr} = q {\bf v}\times{\bf B}.
\end{displaymath}">|; 

$key = q/displaystylefrac{u_3}{gamma,(1-u_1,vslashc^2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2749.png"
 ALT="$\displaystyle \frac{u_3}{\gamma (1-u_1  v/c^2)}.$">|; 

$key = q/displaystylegamma,({{bf{E}_perp+{{bf{v}times{{bf{B}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3098.png"
 ALT="$\displaystyle \gamma ({\bf E}_\perp +{\bf v}\times{\bf B}),$">|; 

$key = q/{displaymath}{mitdiv},{{bf{A}=frac{partialA_x}{partialx}+frac{partialA_y}{partialy}+frac{partialA_z}{partialz}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="\begin{displaymath}
{\mit div} {\bf A} = \frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial y}
+\frac{\partial A_z}{\partial z}
\end{displaymath}">|; 

$key = q/{displaymath}{mitdiv},({{bf{curl},{{bf{A})equiv0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="\begin{displaymath}
{\mit div} ({\bf curl} {\bf A}) \equiv 0.
\end{displaymath}">|; 

$key = q/{displaymath}R_{{rm{load}=R_{{rm{res}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2252.png"
 ALT="\begin{displaymath}
R_{\rm load} = R_{\rm res}.
\end{displaymath}">|; 

$key = q/{{bf{e}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="${\bf e}_y$">|; 

$key = q/{displaymath}C=frac{Q}{V}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="\begin{displaymath}
C = \frac{Q}{V}.
\end{displaymath}">|; 

$key = q/{displaymath}alpha=beta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2566.png"
 ALT="\begin{displaymath}
\alpha=\beta,
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2}frac{1}{4pi,epsilon_0}sum_{i=1}^Nsum_{stackrel{scriptstlejneqi}}^Nfrac{q_i,q_j}{|{{bf{r}_i-{{bf{r}_j|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="73" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="\begin{displaymath}
W =\frac{1}{2} \frac{1}{4\pi \epsilon_0} \sum_{i=1}^N \sum_...
...e j\neq i}}^N
\frac{q_i  q_j}{\vert{\bf r}_i-{\bf r}_j\vert}.
\end{displaymath}">|; 

$key = q/q_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="$q_2$">|; 

$key = q/{displaymath}k_{i,x}=k_{r,x}=k_{t,x}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2506.png"
 ALT="\begin{displaymath}
k_{i x} =k_{r x}= k_{t x}
\end{displaymath}">|; 

$key = q/{{bf{v}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="${\bf v} \cdot d{\bf S}$">|; 

$key = q/j_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$j_x$">|; 

$key = q/{displaymath}dW=-F_z,dz=frac{1}{4pi,epsilon_0}frac{q^2}{4,z^2},dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1517.png"
 ALT="\begin{displaymath}
d W = - F_z dz=\frac{1}{4\pi \epsilon_0} \frac{q^2}{4 z^2} dz.
\end{displaymath}">|; 

$key = q/x>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1601.png"
 ALT="$x&gt;0$">|; 

$key = q/{displaymath}int_P^Qx,y,dl=int_0^1x^2,sqrt{2},dx=frac{sqrt{2}}{3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="\begin{displaymath}
\int_P^Q x y dl = \int_0^1 x^2 \sqrt{2}  dx = \frac{\sqrt{2}}{3}.
\end{displaymath}">|; 

$key = q/epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="$\epsilon_0$">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0,c^3}frac{dot{{bf{u}times{{bf{r}}{r^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3277.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0  c^3} \frac{\dot{\bf u}
\times{\bf r}}{r^2}.$">|; 

$key = q/{displaymath}epsilon=1+frac{n,e^2}{epsilon_0,m_e,(omega_0^{,2}-omega^2)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2322.png"
 ALT="\begin{displaymath}
\epsilon = 1 + \frac{n e^2}{\epsilon_0 m_e (\omega_0^{ 2}-\omega^2)}.
\end{displaymath}">|; 

$key = q/E_{{rm{max}sim0.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3335.png"
 ALT="$E_{\rm max}\sim
0.3$">|; 

$key = q/{displaymath}I=I_Texpleft[-frac{R}{L},(t-T),right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1952.png"
 ALT="\begin{displaymath}
I= I_T \exp \left[ - \frac{R}{L}  (t-T) \right],
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}_2=frac{q_1,q_2}{4pi,epsilon_0}frac{{{bf{r}_2-{{bf{r}_1}{|{{bf{r}_2-{{bf{r}_1|^{3}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="\begin{displaymath}
{\bf f}_2 = \frac{q_1  q_2}{4\pi \epsilon_0} \frac{{\bf r}_2 - {\bf r}_1}
{\vert{\bf r}_2-{\bf r}_1\vert^{3}}
\end{displaymath}">|; 

$key = q/f(x,y)=x,y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$f(x,y)= x y$">|; 

$key = q/{displaymath}langleurangle=leftlanglefrac{{{bf{E}times{{bf{B}cdothat{{bf{z}}{mu_omega}=sqrt{frac{sigma}{8,mu_0,omega}},E_0^{,2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2412.png"
 ALT="\begin{displaymath}
\langle u\rangle = \left\langle \frac{{\bf E}\times{\bf B}\c...
... \omega} = \sqrt{\frac{\sigma}{8 \mu_0 \omega}} E_0^{ 2}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig29.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="225" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig29.eps}}
\end{figure}">|; 

$key = q/kappa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$\kappa$">|; 

$key = q/{displaymath}frac{1}{2},F_{munu}F^{munu}=c^2,B^2-E^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3101.png"
 ALT="\begin{displaymath}
\frac{1}{2}  F_{\mu\nu} F^{\mu\nu} = c^2  B^2 - E^2,
\end{displaymath}">|; 

$key = q/180^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2481.png"
 ALT="$180^\circ$">|; 

$key = q/k_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2383.png"
 ALT="$k_+$">|; 

$key = q/{displaymath}phi(r,theta)=-E_0,r,costheta+E_0,alpha,frac{a^3,costheta}{r^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1736.png"
 ALT="\begin{displaymath}
\phi(r,\theta) = - E_0 r \cos\theta + E_0 \alpha  \frac{a^3 \cos\theta}{r^2}.
\end{displaymath}">|; 

$key = q/displaystyleE_{{rm{total};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="$\displaystyle E_{\rm total}$">|; 

$key = q/displaystyle-F^{ji}=-c,B^{ij},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3045.png"
 ALT="$\displaystyle -F^{ji} = -c B^{ij},$">|; 

$key = q/displaystylefrac{partialA_z}{partialy}-frac{partialA_y}{partialz}=({{rm{i},k_yA_z-{{rm{i},k_zA_y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="$\displaystyle \frac{\partial A_z}{\partial y}
-\frac{\partial A_y}{\partial z} = ({\rm i} k_y A_z - {\rm i} 
k_z A_y)$">|; 

$key = q/deltaxrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2047.png"
 ALT="$\delta x\rightarrow 0$">|; 

$key = q/{displaymath}P=frac{e^2}{6pi,epsilon_0,m_0^{,2},c^3}left(frac{dp}{dt}right)^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img3323.png"
 ALT="\begin{displaymath}
P= \frac{e^2}{6\pi \epsilon_0  m_0^{ 2}  c^3}\left(\frac{dp}{dt}\right)^2.
\end{displaymath}">|; 

$key = q/displaystylefrac{x-v,t}{(1-v^2slashc^2)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2719.png"
 ALT="$\displaystyle \frac{x-v t}{(1-v^2/c^2)^{1/2}},$">|; 

$key = q/displaystyleT^4_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3202.png"
 ALT="$\displaystyle T^4_4$">|; 

$key = q/Q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="$Q'$">|; 

$key = q/{displaymath}{mitPhi}_2=int_{{rm{loop,2}{{bf{B}_1cdotd{{bf{S}_2=int_{{rm{loop,2}f{S}_2=oint_{{rm{loop,2}{{bf{A}_1cdotd{{bf{l}_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="472" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1871.png"
 ALT="\begin{displaymath}
{\mit\Phi}_2 = \int_{\rm loop  2} {\bf B}_1\cdot d{\bf S}_2...
... d{\bf S}_2 = \oint_{\rm loop  2} {\bf A}_1 \cdot
d{\bf l}_2,
\end{displaymath}">|; 

$key = q/omegaggnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2432.png"
 ALT="$\omega\gg \nu$">|; 

$key = q/displaystyle{{bf{b}cdot{{bf{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle {\bf b} \cdot {\bf a},$">|; 

$key = q/{displaymath}{{bf{E}times{{bf{B}=frac{E^2}{c}hat{{bf{k}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2128.png"
 ALT="\begin{displaymath}
{\bf E} \times{\bf B} = \frac{E^2}{c} \hat{\bf k}.
\end{displaymath}">|; 

$key = q/nablaf;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="$\nabla f$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}',t_a)}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{1}{4\pi \epsilon_0} \int \frac{ \rho({\bf r}', t_a)}{\vert{\bf r} - {\bf r}'\vert} 
d^3{\bf r}',
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{A}=-frac{mu_0,I}{4pi}left(,0,,0,,ln[x^2+y^2],right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="\begin{displaymath}
{\bf A} = -\frac{\mu_0  I}{4\pi} \left( 0, 0, \ln[x^2+y^2] \right)
\end{displaymath}">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$h$">|; 

$key = q/displaystylenabla^2{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$\displaystyle \nabla^2{\bf A}$">|; 

$key = q/10^3,{{rm{kg,m}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2289.png"
 ALT="$10^3 {\rm kg m}^{-3}$">|; 

$key = q/K=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2089.png"
 ALT="$K = 1$">|; 

$key = q/{displaymath}k_{pm}simeqkpm{mitDelta}k,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2378.png"
 ALT="\begin{displaymath}
k_{\pm}\simeq k\pm {\mit\Delta} k,
\end{displaymath}">|; 

$key = q/{displaymath}F(Q)=F(P)+int_P^Qleft(f,dx+g,dyright){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="\begin{displaymath}
F(Q) = F(P) + \int_P^Q \left(f dx + g dy\right)
\end{displaymath}">|; 

$key = q/{displaymath}oint_S{{bf{h}cdotd{{bf{S}=-frac{partial}{partialt}left(intc,T,dVright),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="\begin{displaymath}
\oint_S {\bf h}\cdot d{\bf S} = - \frac{\partial}{\partial t}\left(
\int c  T dV\right),
\end{displaymath}">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0}frac{1}{[r+{{bf{r}!cdot!{{bf{u}slashc]},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3123.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0}
\frac{1}{[r+ {\bf r}\!\cdot\!{\bf u}/c]},$">|; 

$key = q/n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2444.png"
 ALT="$n_1$">|; 

$key = q/displaystylefrac{-vslashc^2}{pm(1-v^2slashc^2)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2716.png"
 ALT="$\displaystyle \frac{- v/c^2}{\pm(1-v^2/c^2)^{1/2}}.$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\textstyle =$">|; 

$key = q/{{bf{e}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="${\bf e}_x$">|; 

$key = q/u'=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2762.png"
 ALT="$u'=c$">|; 

$key = q/displaystyle{{bf{B}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2524.png"
 ALT="$\displaystyle {\bf B}_i$">|; 

$key = q/nA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$nA$">|; 

$key = q/{{bf{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1655.png"
 ALT="${\bf d}$">|; 

$key = q/{displaymath}sigma=frac{{{bf{j}}{{{bf{E}}=frac{{{rm{i},n_e,e^2}{m_e,(omega+{{rm{i},nu)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2430.png"
 ALT="\begin{displaymath}
\sigma = \frac{{\bf j}}{{\bf E}} = \frac{{\rm i} n_e e^2}{m_e (\omega+{\rm i} \nu)}.
\end{displaymath}">|; 

$key = q/{displaymath}phi_i({{bf{r})=frac{q_i}{4pi,epsilon_0,|{{bf{r}-{{bf{r}_i|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="\begin{displaymath}
\phi_i({\bf r}) = \frac{q_i}{4\pi \epsilon_0 \vert{\bf r} - {\bf r}_i\vert}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}=q,({{bf{E}+{{bf{v}times{{bf{B}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="\begin{displaymath}
{\bf f} = q  ({\bf E} +{\bf v}\times{\bf B}).
\end{displaymath}">|; 

$key = q/(epsilon_0slash2),E^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="$(\epsilon_0/2)  E^2$">|; 

$key = q/{{bf{v}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="${\bf v}({\bf r})$">|; 

$key = q/{figure}{epsfysize{=3.5in{centerline{epsffile{fig47.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img2135.png"
 ALT="\begin{figure}
\epsfysize =3.5in
\centerline{\epsffile{fig47.eps}}
\end{figure}">|; 

$key = q/displaystyleF_x({{bf{k}cdot{{bf{r}-k,c,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="$\displaystyle F_x ({\bf k}\cdot{\bf r} - k c t),$">|; 

$key = q/{displaymath}partial_muJ^mu=nabla!cdot!{{bf{j}+frac{partialrho}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2965.png"
 ALT="\begin{displaymath}
\partial_\mu J^\mu = \nabla\!\cdot\!{\bf j}
+ \frac{\partial\rho}{\partial t}.
\end{displaymath}">|; 

$key = q/U^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3165.png"
 ALT="$U^\mu$">|; 

$key = q/{{bf{j}=rho,{{bf{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2963.png"
 ALT="${\bf j} =\rho  {\bf u}$">|; 

$key = q/{displaymath}{{bf{E}=-nablaphi-frac{partial{{bf{A}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="\begin{displaymath}
{\bf E} = - \nabla\phi - \frac{\partial {\bf A} }{\partial t}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig6.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="230" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig6.eps}}
\end{figure}">|; 

$key = q/C_k=A_{kij}^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2815.png"
 ALT="$C_k = A_{kij}^{ij}$">|; 

$key = q/{displaymath}int!int{{bf{v}cdotd{{bf{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="\begin{displaymath}
\int\!\int {\bf v}\cdot d{\bf S}
\end{displaymath}">|; 

$key = q/{displaymath}phi_i=frac{1}{4pi,epsilon_0}sum_{stackrel{scriptstylej=1}{scriptscrptstylejneqi}}^Nfrac{q_j}{|{{bf{r}_i-{{bf{r}_j|}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="73" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="\begin{displaymath}
\phi_i = \frac{1}{4\pi \epsilon_0}\sum_{
\stackrel{\scripts...
...tstyle j\neq i}}^N
\frac{q_j}{\vert{\bf r}_i - {\bf r}_j\vert}
\end{displaymath}">|; 

$key = q/D_{perp,1}=D_{perp,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2500.png"
 ALT="$D_{\perp 1} = D_{\perp 2}$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}simeqfrac{e^2,dot{u}^2}{2pi^2,epsilon_0,c^c{[1-(gamma,theta)^2]^2}{[1+(gamma,theta)^2]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3379.png"
 ALT="\begin{displaymath}
\frac{dP(t')}{d{\mit\Omega}} \simeq \frac{e^2  \dot{u}^2}{2...
...^6 \frac{[1-(\gamma \theta)^2]^2}{[1+(\gamma \theta)^2]^5}.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="$\nabla\cdot{\bf A}$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{hst.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img1805.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{hst.eps}}
\end{figure}">|; 

$key = q/{displaymath}E_{parallel,2}-E_{parallel,1}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1693.png"
 ALT="\begin{displaymath}
E_{\parallel 2}-E_{\parallel 1} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right){{bf{E}={{bf{0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="\begin{displaymath}
\left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}\right) {\bf E} = {\bf0},
\end{displaymath}">|; 

$key = q/{displaymath}2pi,r,l,E_r(r)=frac{q,l}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1387.png"
 ALT="\begin{displaymath}
2\pi  r  l E_r(r) = \frac{q l}{\epsilon_0},
\end{displaymath}">|; 

$key = q/rgeqa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="$r\geq a$">|; 

$key = q/displaystyleE_t,{{rm{e}^{,{{rm{i},(k_2,z-omega,t)},hat{{bf{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2457.png"
 ALT="$\displaystyle E_t {\rm e}^{ {\rm i} (k_2 z-\omega t)} \hat{\bf x},$">|; 

$key = q/{displaymath}frac{partialr}{partialx}=frac{x}{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="\begin{displaymath}
\frac{\partial r}{\partial x} = \frac{x}{r}.
\end{displaymath}">|; 

$key = q/k,l=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2091.png"
 ALT="$k l=\pi/2$">|; 

$key = q/{displaymath}nabla^2phi=-frac{rho}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="\begin{displaymath}
\nabla^2 \phi = -\frac{\rho}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{l}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="\begin{displaymath}
\oint_C {\bf E} \cdot d{\bf l} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}A^mu=frac{d^2x^mu}{dtau^2}=frac{dU^mu}{dtau}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2944.png"
 ALT="\begin{displaymath}
A^\mu = \frac{d^2x^\mu}{d\tau^2} = \frac{dU^\mu}{d\tau}
\end{displaymath}">|; 

$key = q/90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$90^\circ$">|; 

$key = q/{displaymath}{{bf{k}_icdot{{bf{r}={{bf{k}_rcdot{{bf{r}={{bf{k}_tcdot{{bf{r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2505.png"
 ALT="\begin{displaymath}
{\bf k}_i\cdot{\bf r} = {\bf k}_r\cdot{\bf r} = {\bf k}_t\cdot{\bf r}
\end{displaymath}">|; 

$key = q/{displaymath}V_1=R_1,I_1+L_1frac{dI_1}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1929.png"
 ALT="\begin{displaymath}
V_1 = R_1  I_1 + L_1 \frac{d I_1}{dt},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig33.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig33.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{{mitDelta}E}{m_0,c^2}=frac{4pi}{3}frac{r_0}{a},beta^3,gamma^4.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img3391.png"
 ALT="\begin{displaymath}
\frac{{\mit\Delta} E}{m_0  c^2} = \frac{4\pi}{3} \frac{r_0}{a}  \beta^3  \gamma^4.
\end{displaymath}">|; 

$key = q/displaystyleoint_S{{bf{B}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="$\displaystyle \oint_S {\bf B} \cdot d{\bf S}$">|; 

$key = q/d{{bf{p}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3312.png"
 ALT="$d{\bf p} = 0$">|; 

$key = q/oint{{bf{v}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$\oint {\bf v}\cdot d{\bf l}$">|; 

$key = q/f(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$f(x,y)$">|; 

$key = q/E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1587.png"
 ALT="$E_0$">|; 

$key = q/{{bf{curl},{{bf{v}=(0,,0,,2,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="${\bf curl} {\bf v} = (0 ,0 ,2 \omega)$">|; 

$key = q/{{bf{j}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="${\bf j}\cdot d{\bf S}$">|; 

$key = q/{displaymath}B_theta=frac{mu_0,I}{2pi,rho}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="\begin{displaymath}
B_\theta = \frac{\mu_0  I}{2\pi  \rho}.
\end{displaymath}">|; 

$key = q/hat{{bf{k}={{bf{k}slashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2443.png"
 ALT="$\hat{\bf k} = {\bf k}/k$">|; 

$key = q/B^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3304.png"
 ALT="$B^\mu$">|; 

$key = q/{displaymath}{{bf{M}={{bf{r}times{{bf{F}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="\begin{displaymath}
{\bf M} = {\bf r}\times{\bf F}.
\end{displaymath}">|; 

$key = q/{{bf{j}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1775.png"
 ALT="${\bf j}_p$">|; 

$key = q/C^{ij}_{klm}=A^{ij}B_{klm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2810.png"
 ALT="$C^{ij}_{klm} = A^{ij}
B_{klm}$">|; 

$key = q/displaystyle+(-a_x,sintheta+a_y,costheta),(-b_x,sintheta+b_y,costheta)+a_z,b_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle +(-a_x \sin\theta + a_y \cos\theta) (-b_x \sin \theta + b_y \cos\theta)
+a_z  b_z$">|; 

$key = q/-deltatheta_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$-\delta\theta_z$">|; 

$key = q/epsilon_{iab};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3025.png"
 ALT="$\epsilon_{iab}$">|; 

$key = q/{displaymath}sigma=left(frac{omega}{omega_0}right)^4,sigma_T,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2306.png"
 ALT="\begin{displaymath}
\sigma = \left(\frac{\omega}{\omega_0}\right)^4 \sigma_T,
\end{displaymath}">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G=-4pi,F(t-t'),delta({{bf{r}-{{bf{r}'),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right)
G = - 4\pi  F(t-t') \delta({\bf r}- {\bf r}'),
\end{displaymath}">|; 

$key = q/-2.2times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1789.png"
 ALT="$-2.2\times 10^{-5}$">|; 

$key = q/{displaymath}-{{bf{E}cdot{{bf{j}=-frac{{{bf{E}cdotnablatimes{{bf{B}}{mu_0}+epsilon_0,{{bf{E}cdotfrac{partial{{bf{E}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2117.png"
 ALT="\begin{displaymath}
- {\bf E} \cdot {\bf j} = - \frac{ {\bf E}\cdot \nabla\times...
...\epsilon_0  {\bf E}\cdot \frac{\partial {\bf E}}{\partial t}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{partialB_y}{partialx}+frac{partialB_x}{partialy}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2588.png"
 ALT="$\displaystyle -\frac{\partial B_y}{\partial x}+
\frac{\partial B_x}{\partial y}.$">|; 

$key = q/{displaymath}P=frac{1}{2},R,|I_0|^{,2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2028.png"
 ALT="\begin{displaymath}
P = \frac{1}{2}  R  \vert I_0\vert^{ 2}.
\end{displaymath}">|; 

$key = q/{displaymath}partial_muequivfrac{partial}{partialx^mu}=left(nabla,frac{1}{c}frac{partial}{partialt}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2907.png"
 ALT="\begin{displaymath}
\partial_\mu \equiv \frac{\partial}{\partial x^\mu} = \left(\nabla,
\frac{1}{c}\frac{\partial}{\partial t}\right),
\end{displaymath}">|; 

$key = q/{displaymath}int_Vnablacdot{{bf{E},,d^3{{bf{r}=frac{q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="\begin{displaymath}
\int_V \nabla \cdot{\bf E}  d^3{\bf r}= \frac{q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=frac{e}{4pi,epsilon_0}frac{1-u^2slashc^2}{r_0^{~3}(1-u^2slashc^2+u_r^{~2}slashc^2)^{3slash2}},{{bf{r}_0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3264.png"
 ALT="\begin{displaymath}
{\bf E} = \frac{e}{4\pi \epsilon_0} \frac{1-u^2/c^2}{r_0^{&nbsp;3}(1-u^2/c^2 +
u_r^{&nbsp;2}/c^2)^{3/2}} {\bf r}_0,
\end{displaymath}">|; 

$key = q/displaystyle-xsintheta+ycostheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle -x\sin\theta + y\cos\theta,$">|; 

$key = q/(1slash2),C,V^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="$(1/2)  C V^2$">|; 

$key = q/{displaymath}F_{munu}=-F_{numu}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3031.png"
 ALT="\begin{displaymath}
F_{\mu\nu} = -F_{\nu\mu}.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot({{bf{A}times{{bf{B})={{bf{B}cdotnablatimes{{bf{A}-{{bf{A}cdotnablatimes{{bf{B}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="\begin{displaymath}
\nabla\cdot({\bf A}\times{\bf B}) = {\bf B}\cdot \nabla\times{\bf A} - {\bf A}\cdot
\nabla\times{\bf B}
\end{displaymath}">|; 

$key = q/displaystylealpha,betaleft(frac{2}{alpha+beta}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2562.png"
 ALT="$\displaystyle \alpha \beta\left(\frac{2}{\alpha+\beta}\right)^2,$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}},d{mitOmega}=-frac{dE(theta,varphi)}{dt'},0,c,E_{{rm{rad}^{,2},frac{s}{r},r^2,d{mitOmega},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img3341.png"
 ALT="\begin{displaymath}
\frac{dP(t')}{d{\mit\Omega}}
 d{\mit\Omega} = -\frac{dE(\th...
..., c  E_{\rm rad}^{ 2}
 \frac{s}{r} 
r^2  d{\mit \Omega},
\end{displaymath}">|; 

$key = q/{displaymath}I(x,t)=frac{V_0}{sqrt{LslashC}}cos(omega,t-k,x).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img2061.png"
 ALT="\begin{displaymath}
I(x, t) = \frac{V_0}{\sqrt{L/C}} \cos(\omega  t -k x).
\end{displaymath}">|; 

$key = q/6times10^{7},(Omega,{{rm{m})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2413.png"
 ALT="$6\times
10^{7} (\Omega {\rm m})^{-1}$">|; 

$key = q/displaystyleu_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2736.png"
 ALT="$\displaystyle u_1'$">|; 

$key = q/{displaymath}nabla^2(u_1+u_2)=nabla^2u_1+nabla^2u_2=v_1+v_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="\begin{displaymath}
\nabla^2(u_1+u_2) = \nabla^2 u_1 + \nabla^2 u_2 = v_1 + v_2.
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}=L,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1883.png"
 ALT="\begin{displaymath}
{\mit\Phi} = L  I.
\end{displaymath}">|; 

$key = q/I=I_{{rm{max}costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$I= I_{\rm max}\cos\theta$">|; 

$key = q/oint_C{{bf{B}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="$\oint_C {\bf B} \cdot d{\bf l}$">|; 

$key = q/{{bf{a}cdot{{bf{c}=a_x,c_x+a_y,c_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="${\bf a}\cdot {\bf c} = a_x  c_x + a_y  c_y$">|; 

$key = q/{displaymath}intdelta({{bf{r}),d^3{{bf{r}=1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="\begin{displaymath}
\int \delta({\bf r}) d^3{\bf r} =1,
\end{displaymath}">|; 

$key = q/langle{{bf{m}_irangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1770.png"
 ALT="$\langle {\bf m}_i\rangle$">|; 

$key = q/displaystyle(-a_x,sintheta+a_y,costheta),b_z-a_z,(-b_x,sintheta+b_y,costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle (-a_x  \sin\theta + a_y \cos\theta) b_z - a_z (-b_x  \sin\theta + b_y \cos\theta)$">|; 

$key = q/r=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$r=$">|; 

$key = q/{displaymath}{{bf{E}_3=-nablaphi_3,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1442.png"
 ALT="\begin{displaymath}
{\bf E}_3 = -\nabla\phi_3,
\end{displaymath}">|; 

$key = q/displaystyle{{rm{i},frac{omega}{c^2},E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2587.png"
 ALT="$\displaystyle {\rm i} \frac{\omega}{c^2} E_z$">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1861.png"
 ALT="$H$">|; 

$key = q/beta=-uslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3116.png"
 ALT="$\beta=-u/c$">|; 

$key = q/displaystyleA_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="$\displaystyle A_z$">|; 

$key = q/displaystyle({{bf{a}times{{bf{b})^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle ({\bf a}\times{\bf b})^2$">|; 

$key = q/{displaymath}frac{partial^2U}{partialx^2}=frac{partial}{partialx}frac{partialV}{frac{partial}{partialy}frac{partialU}{partialy},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1561.png"
 ALT="\begin{displaymath}
\frac{\partial^2 U}{\partial x^2} = \frac{\partial}{\partial...
... - \frac{\partial}{\partial y} \frac{\partial U}
{\partial y},
\end{displaymath}">|; 

$key = q/|A|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="$\vert A\vert$">|; 

$key = q/{displaymath}nablacdot{{bf{E},,dx,dy,dz=frac{Q}{epsilon_0}=frac{rho,dx,dy,dz}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="\begin{displaymath}
\nabla \cdot {\bf E}   dx dy dz = \frac{Q}{\epsilon_0}=
\frac{\rho dx dy dz}{\epsilon_0},
\end{displaymath}">|; 

$key = q/x^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2893.png"
 ALT="$x^1$">|; 

$key = q/{displaymath}frac{{{bf{E}!cdot!{{bf{j}}{c}=-partial_iT^{i4}-partial_4T^{44}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3212.png"
 ALT="\begin{displaymath}
\frac{{\bf E}\!\cdot \!{\bf j}}{c} = - \partial_i T^{i4} - \partial_4 T^{44}.
\end{displaymath}">|; 

$key = q/int{{bf{curl},{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$\int {\bf curl} {\bf A}\cdot d{\bf S}$">|; 

$key = q/a<r<b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1386.png"
 ALT="$a&lt;r&lt;b$">|; 

$key = q/displaystyleE_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3278.png"
 ALT="$\displaystyle E_\theta$">|; 

$key = q/displaystyle-frac{sigma}{2,epsilon_0}mbox{hspace{2cm}below}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$\displaystyle -\frac{\sigma}{2 \epsilon_0}\mbox{\hspace{2cm} below}.$">|; 

$key = q/{displaymath}I=A_mu,B^mu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3301.png"
 ALT="\begin{displaymath}
I = A_\mu  B^\mu,
\end{displaymath}">|; 

$key = q/0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2420.png"
 ALT="$0.2$">|; 

$key = q/{mitOmega}=e,B_0slashm_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2364.png"
 ALT="${\mit \Omega} = e B_0/m_e$">|; 

$key = q/langlecos(omega,t),cos(omega,t)rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2022.png"
 ALT="$\langle \cos(\omega  t)  \cos(\omega  t)\rangle = 1/2$">|; 

$key = q/displaystyle2,delta_b^k.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3009.png"
 ALT="$\displaystyle 2 \delta_b^k.$">|; 

$key = q/{{bf{r}_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="${\bf r}_N$">|; 

$key = q/[(nablacdot{{bf{E}),{{bf{E}]_i=(partialE_jslashpartialx_j),E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2189.png"
 ALT="$[(\nabla\cdot{\bf E}) {\bf E}]_i = (\partial E_j/\partial x_j) E_i$">|; 

$key = q/displaystyleB_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="$\displaystyle B_\theta$">|; 

$key = q/{displaymath}{{bf{v}=mbox{{boldmath{{omega{}times{{bf{r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="\begin{displaymath}
{\bf v} = \mbox{\boldmath$\omega$}\times {\bf r}
\end{displaymath}">|; 

$key = q/{displaymath}c=frac{a^2}{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1532.png"
 ALT="\begin{displaymath}
c = \frac{a^2}{b}.
\end{displaymath}">|; 

$key = q/A_i^j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2817.png"
 ALT="$A_i^j$">|; 

$key = q/{displaymath}{{bf{u}=frac{{{bf{E}times{{bf{B}}{mu_0}=frac{omega^2,l^2,I_0^{,2}}{ga(t-rslashc)],frac{sin^2theta}{r^2},hat{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="394" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2229.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{ {\bf E} \times{\bf B}}{\mu_0} = \frac{\omeg...
...sin^2[\omega(t-r/c)]  \frac{\sin^2\theta}{r^2} 
\hat{\bf r}.
\end{displaymath}">|; 

$key = q/nablaequiv(partialslashpartialx,,partialslashpartialy,,partialslashpartialz);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="$\nabla\equiv (\partial/\partial x, \partial/\partial y,  
\partial/\partial z)$">|; 

$key = q/m=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1649.png"
 ALT="$m=1$">|; 

$key = q/a>b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2626.png"
 ALT="$a&gt;b$">|; 

$key = q/{displaymath}{{bf{E}_{{rm{induction}=frac{e}{4pi,epsilon_0}frac{1-u^2slashc^2}{s^3},{{bf{r}_u.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3263.png"
 ALT="\begin{displaymath}
{\bf E}_{\rm induction} = \frac{e}{4\pi \epsilon_0}
\frac{1-u^2/c^2}{s^3} {\bf r}_u.
\end{displaymath}">|; 

$key = q/{displaymath}-nabla^2phi-frac{partial,nablacdot{{bf{A}}{partialt}=frac{rho}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="\begin{displaymath}
-\nabla^2 \phi -
\frac{\partial  \nabla\cdot{\bf A}}{\partial t} = \frac{\rho}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/{displaymath}phi(x,y)=X(x),Y(y).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1606.png"
 ALT="\begin{displaymath}
\phi(x, y) = X(x)  Y(y).
\end{displaymath}">|; 

$key = q/phi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\phi(t)$">|; 

$key = q/1slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2160.png"
 ALT="$1/3$">|; 

$key = q/{displaymath}int!int_Sf(x,y,z),dS=lim_{deltaS_irightarrow0}sum_if(x,y,z),deltaS_i{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="\begin{displaymath}
\int\!\int_S f(x,y,z)  dS = \lim_{\delta S_i\rightarrow 0}\sum_i f(x,y,z) 
\delta S_i
\end{displaymath}">|; 

$key = q/VslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1902.png"
 ALT="$V/R$">|; 

$key = q/{displaymath}A_x(x+dx),dy,dz-A_x(x),dy,dz=frac{partialA_x}{partialx},dx,dy,dz=frac{partialA_x}{partialx},dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="\begin{displaymath}
A_x(x+dx)  dy dz - A_x(x)  dy dz = \frac{\partial A_x}{\partial x} dx dy dz
= \frac{\partial A_x}{\partial x} dV,
\end{displaymath}">|; 

$key = q/{{bf{S}=S,(cosalpha,,sinalpha,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="${\bf S} = S (\cos\alpha,  \sin\alpha,  0)$">|; 

$key = q/{displaymath}int_0^1x^2,dxint_0^{1-x}y,dy=int_0^1frac{x^2}{2},(1-x)^2,dx=frac{1}{60}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="\begin{displaymath}
\int_0^1 x^2 dx \int_0^{1-x} y dy = \int_0^1\frac{x^2}{2}  (1-x)^2 dx
= \frac{1}{60}.
\end{displaymath}">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="$\rho$">|; 

$key = q/{displaymath}{{bf{B}simeq-frac{omega,l,I_0}{4pi,epsilon_0,c^3},sintheta,frac{sina(t-rslashc)]}{r},hat{mbox{{boldmath{{varphi{}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2225.png"
 ALT="\begin{displaymath}
{\bf B} \simeq -\frac{\omega  l  I_0 }{4\pi  \epsilon_0 \...
...c{\sin
[\omega (t-r/c)]}{r}  \hat{\mbox{\boldmath$\varphi$}}.
\end{displaymath}">|; 

$key = q/omega_{mn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2625.png"
 ALT="$\omega_{mn}$">|; 

$key = q/displaystylemu_0,{{bf{j}+frac{1}{c^2}frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="$\displaystyle \mu_0 {\bf j} + \frac{1}{c^2} \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/r=b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2646.png"
 ALT="$r=b$">|; 

$key = q/F_y(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="$F_y(\phi)$">|; 

$key = q/{displaymath}A^mu=gammaleft(frac{dgamma}{dt},{{bf{u}+gamma,{{bf{a},c,frac{dgamma}{dt}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3150.png"
 ALT="\begin{displaymath}
A^\mu = \gamma\left(\frac{d\gamma}{dt} {\bf u} + \gamma  {\bf a},
c \frac{d\gamma}{dt}\right).
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{E}=frac{rho}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="\begin{displaymath}
\nabla \cdot {\bf E} = \frac{\rho}{\epsilon_0}.
\end{displaymath}">|; 

$key = q/dS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$dS$">|; 

$key = q/{displaymath}U=frac{epsilon_0}{2},E^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="\begin{displaymath}
U = \frac{\epsilon_0}{2}  E^2.
\end{displaymath}">|; 

$key = q/{displaymath}F^{munu}=leftlgrouparray{{cccc}0&-c,B_z&+c,B_y&+E_x[0.5ex]+c,B_z&0&&0&+E_z[0.5ex]-E_x&-E_y&-E_z&0array{rightrgroup.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="111" BORDER="0"
 SRC="|."$dir".q|img3046.png"
 ALT="\begin{displaymath}
F^{\mu\nu} = \left\lgroup \begin{array}{cccc}
0 &amp; -c B_z &amp; ...
...+E_z [0.5ex]
-E_x &amp; -E_y &amp;-E_z &amp; 0\end{array}\right
\rgroup.
\end{displaymath}">|; 

$key = q/g^{ij}=g^{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2836.png"
 ALT="$g^{ij} = g^{ji}$">|; 

$key = q/{displaymath}frac{1}{2},L_1,I_1^{,2}+frac{1}{2},L_2,I_2^{,2}+M,I_1,I_2geq0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1966.png"
 ALT="\begin{displaymath}
\frac{1}{2}  L_1  I_1^{ 2} + \frac{1}{2}  L_2  I_2^{ 2} + M  I_1  I_2\geq 0,
\end{displaymath}">|; 

$key = q/displaystyleE_{{rm{sheet};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="$\displaystyle E_{\rm sheet}$">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}intE^2,d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \int E^2 d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}rho({{bf{r},t)=intintdelta({{bf{r}-{{bf{r}')delta(t-t'),rho({{bf{r}',t'),d^3{{bf{r}'dt'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="\begin{displaymath}
\rho({\bf r}, t) = \int\int \delta({\bf r} - {\bf r}') \delta(t-t')  
\rho({\bf r}', t') d^3 {\bf r}' dt'.
\end{displaymath}">|; 

$key = q/B_{y,1}=B_{y,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2552.png"
 ALT="$B_{y 1}= B_{y 2}$">|; 

$key = q/g_{ij}=g_{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2831.png"
 ALT="$g_{ij} = g_{ji}$">|; 

$key = q/psi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2981.png"
 ALT="$\psi=0$">|; 

$key = q/displaystyleAexp(k,x)+Bexp(-k,x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1617.png"
 ALT="$\displaystyle A \exp(k x) + B \exp(-k x),$">|; 

$key = q/x+deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2041.png"
 ALT="$x+\delta x$">|; 

$key = q/displaystylefrac{u,a_0}{c^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3154.png"
 ALT="$\displaystyle \frac{u a_0}{c^2}.$">|; 

$key = q/dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2660.png"
 ALT="$dt$">|; 

$key = q/displaystylefrac{d{{bf{u}}{dt'}=-dot{u},(cosphi,,sinphi,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3361.png"
 ALT="$\displaystyle \frac{d{\bf u}}{dt'} = -\dot{u} (\cos\phi,  \sin\phi,  0),$">|; 

$key = q/{displaymath}nablatimes(phi,{{bf{A})=phi,nablatimes{{bf{A}+nablaphitimes{{bf{A}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="\begin{displaymath}
\nabla\times(\phi {\bf A}) =\phi  \nabla\times{\bf A} +\nabla\phi\times{\bf A}
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{H}!cdot!d{{bf{l}=int_S{{bf{j}_t!cdot!d{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1783.png"
 ALT="\begin{displaymath}
\oint_C {\bf H}\!\cdot\!d{\bf l} = \int_S {\bf j}_t\!\cdot\!d{\bf S}.
\end{displaymath}">|; 

$key = q/displaystyleB=D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2713.png"
 ALT="$\displaystyle B=D$">|; 

$key = q/(A)^2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2845.png"
 ALT="$(A)^2=0$">|; 

$key = q/displaystylefrac{x-x'}{[(x-x')^2+(y-y')^2+(z-z')^2]^{,3slash2}}=mbox{hspace{4cm}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="504" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$\displaystyle \frac{x - x'}{[(x-x')^2+(y-y')^2 + (z-z')^2]^{ 3/2}} = \mbox{\hspace{4cm}}$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intleft(frac{[{{bf{j}]times{{bf{R}}{R^3}+frac{[partial{{bf{j}slashpartialt]times{{bf{R}}{c,R^2}right)dV'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \left(
\frac{ [{\bf j}]\times {\bf R} }{R^3} + \frac{ [\partial {\bf j}/\partial t]\times {\bf R} }
{c R^2} \right)dV'.$">|; 

$key = q/displaystyle|V_0|,cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2015.png"
 ALT="$\displaystyle \vert V_0\vert  \cos(\omega  t),$">|; 

$key = q/{displaymath}L,C,frac{partial^2V}{partialt^2}=frac{partial^2V}{partialx^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2054.png"
 ALT="\begin{displaymath}
L C \frac{\partial^2 V}{\partial t^2} = \frac{\partial^2 V}{\partial x^2}.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi}intfrac{C_y({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="$\displaystyle \frac{1}{4\pi } \int\frac{C_y({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'},$">|; 

$key = q/n_2=1.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2565.png"
 ALT="$n_2=1.5$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig28.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig28.eps}}
\end{figure}">|; 

$key = q/displaystyleoint_{S}{{bf{E}_1cdotd{{bf{S}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1433.png"
 ALT="$\displaystyle \oint_{S} {\bf E}_1\cdot d{\bf S}_i$">|; 

$key = q/{displaymath}V_2=M,frac{dI_1}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1932.png"
 ALT="\begin{displaymath}
V_2 = M  \frac{d I_1}{dt},
\end{displaymath}">|; 

$key = q/{displaymath}A_{{rm{eff}=frac{l^2}{4,epsilon_0,c,R_{{rm{rad}}=frac{3}{8pi},lambda^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2260.png"
 ALT="\begin{displaymath}
A_{\rm eff} = \frac{l^2}{4 \epsilon_0  c  R_{\rm rad}} = \frac{3}{8\pi} \lambda^2.
\end{displaymath}">|; 

$key = q/E_z=B_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2637.png"
 ALT="$E_z=B_z=0$">|; 

$key = q/{displaymath}nablaUcdotnablaV=frac{partialV}{partialy}frac{partialV}{partialx}-fc{partialV}{partialx}frac{partialV}{partialy}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1570.png"
 ALT="\begin{displaymath}
\nabla U \cdot \nabla V = \frac{\partial V}{\partial y}\frac...
...\frac{\partial V}{\partial x} \frac{\partial V}{\partial y}=0.
\end{displaymath}">|; 

$key = q/displaystylephi(x,pi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1599.png"
 ALT="$\displaystyle \phi(x, \pi)$">|; 

$key = q/{displaymath}B_g=frac{N,I}{(2pi,a-d)slashmu+dslashmu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1844.png"
 ALT="\begin{displaymath}
B_g = \frac{N I}{(2\pi a-d)/\mu + d/\mu_0}.
\end{displaymath}">|; 

$key = q/+v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2728.png"
 ALT="$+v$">|; 

$key = q/{{bf{g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3224.png"
 ALT="${\bf g}$">|; 

$key = q/x^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2894.png"
 ALT="$x^3$">|; 

$key = q/{displaymath}A_z({{bf{r},t)simeqfrac{mu_0}{4pi}int_{-lslash2}^{lslash2}frac{I(z',t-rslashc)}{r},dz'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2218.png"
 ALT="\begin{displaymath}
A_z ({\bf r}, t) \simeq \frac{\mu_0}{4\pi} \int_{-l/2}^{l/2} \frac{I(z', t -r/c)}{r} dz'.
\end{displaymath}">|; 

$key = q/n_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2953.png"
 ALT="$n_0$">|; 

$key = q/displaystyle{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="$\displaystyle {\bf B}$">|; 

$key = q/N_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1661.png"
 ALT="$N_i$">|; 

$key = q/U_muA^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2951.png"
 ALT="$U_\mu A^\mu$">|; 

$key = q/{displaymath}g_{munu}=g_{mu'nu'},p_{mu}^{mu'},p_{nu}^{nu'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2917.png"
 ALT="\begin{displaymath}
g_{\mu\nu} = g_{\mu'\nu'} p_{\mu}^{\mu'}  p_{\nu}^{\nu'}.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{A}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf A} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{S}=sum_idelta{{bf{S}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="\begin{displaymath}
{\bf S} = \sum_i \delta {\bf S}_i.
\end{displaymath}">|; 

$key = q/dV=A,dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="$dV = A  dx$">|; 

$key = q/x^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2778.png"
 ALT="$x^i$">|; 

$key = q/L_1,dI_1slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1922.png"
 ALT="$L_1  d I_1/dt$">|; 

$key = q/{{bf{curl},{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="${\bf curl} {\bf v}$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{[partial{{bf{j}_perpslashpartialt]times{{bf{R}}{c,R^2},dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \frac{ [\partial {\bf j}_\perp/\partial t]\times {\bf R} }
{c R^2} dV',$">|; 

$key = q/{displaymath}|{{bf{f}_2|proptofrac{1}{|{{bf{r}_2-{{bf{r}_1|^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="\begin{displaymath}
\vert{\bf f}_2\vert \propto \frac{1}{\vert{\bf r}_2- {\bf r}_1\vert^2}.
\end{displaymath}">|; 

$key = q/displaystyle2,x,y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1546.png"
 ALT="$\displaystyle 2  x y.$">|; 

$key = q/hat{{bf{k}=-hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2448.png"
 ALT="$\hat{\bf k} = -\hat{\bf z}$">|; 

$key = q/{displaymath}frac{partial}{partialt}=frac{r}{s}frac{partial}{partialt'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3247.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial t} = \frac{r}{s} \frac{\partial}{\partial t'}.
\end{displaymath}">|; 

$key = q/{displaymath}C_n=frac{2,phi_0}{pi}int_0^pisin(n,y),,dy=frac{2,phi_0}{n,pi},[1-cos(n,pi)],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1638.png"
 ALT="\begin{displaymath}
C_n = \frac{2 \phi_0}{\pi} \int_0^\pi \sin (n y)  dy
= \frac{2 \phi_0}{n  \pi}  [1- \cos (n \pi) ],
\end{displaymath}">|; 

$key = q/nablacdot{{bf{C}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$\nabla\cdot {\bf C} = 0$">|; 

$key = q/{displaymath}{{bf{B}=mu,{{bf{H},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1794.png"
 ALT="\begin{displaymath}
{\bf B} = \mu {\bf H},
\end{displaymath}">|; 

$key = q/B_1>B_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1830.png"
 ALT="$B_1 &gt; B_0$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{mc.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="415" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img1832.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{mc.eps}}
\end{figure}">|; 

$key = q/nablacdot{{bf{j}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="$\nabla\cdot{\bf j} = 0$">|; 

$key = q/{displaymath}{{bf{B}=frac{mu_0}{4pi}intleft(frac{[{{bf{j}]times{{bf{R}}{R^3}+fraf{j}slashpartialt]times{{bf{R}}{cR^2}right),dV',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="\begin{displaymath}
{\bf B} = \frac{\mu_0}{4\pi} \int \left(
\frac{ [{\bf j}]\ti...
...rtial {\bf j}/\partial t]\times {\bf R} }
{cR^2} \right) dV',
\end{displaymath}">|; 

$key = q/{{bf{curl,A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="${\bf curl  A}$">|; 

$key = q/phirightarrow-E_0,r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1645.png"
 ALT="$\phi\rightarrow -E_0 r \cos\theta$">|; 

$key = q/xrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1605.png"
 ALT="$x\rightarrow \infty$">|; 

$key = q/r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3117.png"
 ALT="$r'$">|; 

$key = q/{nabla}cdot{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="${\nabla}\cdot {\bf E}$">|; 

$key = q/displaystyleV(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2007.png"
 ALT="$\displaystyle V(t)$">|; 

$key = q/(R)^2=R_muR^mu=-r^2+c^2,t^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2898.png"
 ALT="$(R)^2 = R_\mu R^\mu = -r^2 + c^2  t^2$">|; 

$key = q/theta_0=pmpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3377.png"
 ALT="$\theta_0=\pm \pi/2$">|; 

$key = q/-mu_0,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="$-\mu_0  I$">|; 

$key = q/displaystylephi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1405.png"
 ALT="$\displaystyle \phi_2$">|; 

$key = q/{A^i}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2840.png"
 ALT="${A^i}_j$">|; 

$key = q/dllsqrt{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="$d\ll \sqrt{A}$">|; 

$key = q/{displaymath}nabla(phi,psi)=phi,nablapsi+psi,nablaphi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="\begin{displaymath}
\nabla(\phi  \psi) = \phi  \nabla\psi + \psi  \nabla \phi.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{P}({{bf{r})=sum_iN_ilangle{{bf{p}_irangle,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1659.png"
 ALT="\begin{displaymath}
{\bf P}({\bf r}) = \sum_i N_i \langle {\bf p}_i\rangle,
\end{displaymath}">|; 

$key = q/displaystylefrac{t-v,xslashc^2}{(1-v^2slashc^2)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2720.png"
 ALT="$\displaystyle \frac{t-v x/c^2}{(1-v^2/c^2)^{1/2}}.$">|; 

$key = q/x+dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1662.png"
 ALT="$x+dx$">|; 

$key = q/Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2037.png"
 ALT="$Z$">|; 

$key = q/{displaymath}nabla^2psi=v.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="\begin{displaymath}
\nabla^2\psi = v.
\end{displaymath}">|; 

$key = q/{displaymath}0=mu_0,nablacdot{{bf{j}+lambda,frac{partial,nablacdot{{bf{E}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="\begin{displaymath}
0= \mu_0  \nabla\cdot{\bf j} +\lambda  \frac{\partial 
\nabla\cdot{\bf E}}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}W=int_{infty}^aleft(-frac{1}{x^2}right),dx=left[frac{1}{x}right]_{infty}^a=frac{1}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="\begin{displaymath}
W = \int_{\infty}^a \left(-\frac{1}{x^2}\right) dx = \left[\frac{1}{x}\right]_{\infty}^a
=\frac{1}{a}.
\end{displaymath}">|; 

$key = q/a<b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1384.png"
 ALT="$a&lt;b$">|; 

$key = q/{{bf{a},{{rm{x},{{bf{b}=(1slash2,,-1slash2,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="${\bf a}  {\rm x}  {\bf b} = (1/2,  -1/2, 0)$">|; 

$key = q/I=N,q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="$I= N q$">|; 

$key = q/{displaymath}frac{4pi}{mu_0,e},{{bf{B}=-frac{{{bf{r}times{{bf{u}}{s^2,r}-frac{{{r}!cdot!dot{{bf{u}}{c}-frac{u^2}{c}right)right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3258.png"
 ALT="\begin{displaymath}
\frac{4\pi}{\mu_0 e}  {\bf B} =
-\frac{{\bf r}\times{\bf u...
...{\bf r}\!\cdot\!\dot{\bf u}}{c} - \frac{u^2}{c}\right)\right],
\end{displaymath}">|; 

$key = q/E_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="$E_\perp$">|; 

$key = q/{displaymath}dF(x,y)=f(x,y),dx+g(x,y),dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="\begin{displaymath}
dF(x,y) = f(x,y) dx + g(x,y) dy.
\end{displaymath}">|; 

$key = q/lambdasim3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2040.png"
 ALT="$\lambda \sim 3$">|; 

$key = q/{displaymath}nabla^2G({{bf{r},,{{bf{r}')=delta({{bf{r}-{{bf{r}'){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="\begin{displaymath}
\nabla^2 G({\bf r},  {\bf r}') = \delta({\bf r} - {\bf r}')
\end{displaymath}">|; 

$key = q/{displaymath}sintheta_i=frac{beta}{sqrt{1+beta^2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2568.png"
 ALT="\begin{displaymath}
\sin\theta_i = \frac{\beta}{\sqrt{1+\beta^2}},
\end{displaymath}">|; 

$key = q/{displaymath}S_{x'}=S,cos,(alpha-theta)=S,cosalpha,costheta+S,sinalpha,sintheta=S_x,costheta+S_y,sintheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="\begin{displaymath}
S_{x'} = S \cos (\alpha-\theta) = S \cos\alpha \cos\thet...
...S \sin\alpha \sin\theta
= S_x \cos\theta + S_y \sin\theta,
\end{displaymath}">|; 

$key = q/{displaymath}Box^2uequivleft(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)u=v.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="\begin{displaymath}
\Box^2 u \equiv \left(\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right) u = v.
\end{displaymath}">|; 

$key = q/phirightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2648.png"
 ALT="$\phi\rightarrow\infty$">|; 

$key = q/G^{ij}=T^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3219.png"
 ALT="$G^{ij} = T^{ij}$">|; 

$key = q/displaystylea_xcostheta+a_ysintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle a_x\cos\theta + a_y\sin \theta,$">|; 

$key = q/{displaymath}{{bf{u}=frac{E^2}{mu_0,c},hat{{bf{k}=epsilon_0,c,E^2,hat{{bf{k}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2129.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{E^2}{\mu_0  c}  \hat{\bf k} = \epsilon_0  c  E^2  \hat{\bf k}.
\end{displaymath}">|; 

$key = q/F(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$F(x,y)$">|; 

$key = q/F_{munu}=-F_{numu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3062.png"
 ALT="$F_{\mu\nu}=-F_{\nu\mu}$">|; 

$key = q/displaystylegammaleft(phi'+frac{u}{c},c,A_1'right)=frac{gamma,e}{4pi,epsilon_0,r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3115.png"
 ALT="$\displaystyle \gamma\left(\phi' + \frac{u }{c}  c A_1'\right)= \frac{\gamma  e}
{4\pi  \epsilon_0 r'},$">|; 

$key = q/displaystylefrac{partialE_x}{partialx}+frac{partialE_y}{partialy}+{{rm{i},k,E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2575.png"
 ALT="$\displaystyle \frac{\partial E_x}{\partial x} + \frac{\partial E_y}{\partial y} + {\rm i} k E_z$">|; 

$key = q/{displaymath}P'=frac{dE'}{dt'}=frac{dE}{dt}=P,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img3315.png"
 ALT="\begin{displaymath}
P' = \frac{dE'}{dt'} = \frac{dE}{dt} = P,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}_2=-G,m_1,m_2,frac{{{bf{r}_2-{{bf{r}_1}{|{{bf{r}_2-{{bf{r}_1|^{3}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="\begin{displaymath}
{\bf f}_2 = - G  m_1  m_2  \frac{{\bf r}_2 - {\bf r}_1}
{\vert{\bf r}_2 - {\bf r}_1\vert^{3}}
\end{displaymath}">|; 

$key = q/{{bf{B}_1={{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1471.png"
 ALT="${\bf B}_1={\bf B}_2$">|; 

$key = q/{displaymath}t_r=t-|{{bf{r}-{{bf{r}'|slashc{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="\begin{displaymath}
t_r = t - \vert{\bf r} - {\bf r}'\vert/c
\end{displaymath}">|; 

$key = q/delta(x-x_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="$\delta(x-x_0)$">|; 

$key = q/displaystyleX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1616.png"
 ALT="$\displaystyle X$">|; 

$key = q/l,(a_1,x'+b_1,y'+c_1,z'+d_1,t'+e_1)+m,(a_2,x'+cdots)+n,(a_3,x'+cdots)+p=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="606" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2692.png"
 ALT="$l (a_1  x' + b_1  y'
+c_1  z' +d_1  t' + e_1) + m (a_2  x' +\cdots) +n (a_3  x'+\cdots) + p =0$">|; 

$key = q/{displaymath}frac{P}{dEslashdt}=frac{e^2}{6pi,epsilon_0,m_0^{,2},c^3}frac{1}{u}f,epsilon_0,m_0,c^2}frac{1}{m_0,c^2}frac{dE}{dx},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3325.png"
 ALT="\begin{displaymath}
\frac{P}{dE/dt} = \frac{e^2}{6\pi \epsilon_0  m_0^{ 2}  ...
...\pi \epsilon_0  m_0  c^2}\frac{1}{m_0  c^2}
\frac{dE}{dx},
\end{displaymath}">|; 

$key = q/displaystyleT^{4i}=frac{({{bf{E}times{{bf{B})^i}{mu_0,c},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3209.png"
 ALT="$\displaystyle T^{4i} = \frac{({\bf E}\times{\bf B})^i}{\mu_0  c},$">|; 

$key = q/{displaymath}int!int!int_Vf(x,y,z),dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="\begin{displaymath}
\int\!\int\!\int_V f(x,y,z) dV,
\end{displaymath}">|; 

$key = q/dS=dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$dS=dy dz$">|; 

$key = q/dt'>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2668.png"
 ALT="$dt'&gt;0$">|; 

$key = q/displaystyley,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2655.png"
 ALT="$\displaystyle y,$">|; 

$key = q/R_1=sqrt{r^2+(d-z)^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1707.png"
 ALT="$R_1= \sqrt{r^2+(d-z)^2}$">|; 

$key = q/(nablatimes{{bf{B})_x=(nablatimes{{bf{B})_y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="$(\nabla\times{\bf B})_x
=(\nabla\times{\bf B})_y = 0$">|; 

$key = q/{displaymath}dT=frac{partialT}{partialx},dx+frac{partialT}{partialy},dy+frac{partialT}{partialz},dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="\begin{displaymath}
dT = \frac{\partial T}{\partial x} dx +\frac{\partial T}{\partial y} dy+
\frac{\partial T}{\partial z} dz.
\end{displaymath}">|; 

$key = q/B_0(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2389.png"
 ALT="$B_0(z)$">|; 

$key = q/R^mu=(x^1,x^2,x^3,x^4);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2895.png"
 ALT="$R^\mu= (x^1, x^2, x^3, x^4)$">|; 

$key = q/{{bf{A}={{bf{grad},phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="${\bf A} = {\bf grad} \phi$">|; 

$key = q/displaystyleT^{4'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2886.png"
 ALT="$\displaystyle T^{4'}$">|; 

$key = q/displaystylenabla^2W_x=-C_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="$\displaystyle \nabla^2 W_x = - C_x,$">|; 

$key = q/{displaymath}x=r,sintheta,cosphi,~~~y=r,sintheta,sinphi,~~~z=r,costheta,~~~dV=r^2,sintheta,dr,dtheta,dphi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="587" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="\begin{displaymath}
x = r \sin\theta \cos\phi,&nbsp;&nbsp;&nbsp;y = r \sin\theta \sin\phi,&nbsp;&nbsp;&nbsp;z = r \cos\theta,&nbsp;&nbsp;&nbsp;dV = r^2 \sin\theta dr d\theta d\phi
\end{displaymath}">|; 

$key = q/RrightarrowZ_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2101.png"
 ALT="$R\rightarrow Z_1$">|; 

$key = q/{displaymath}D_{perp,2}-D_{perp,1}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1690.png"
 ALT="\begin{displaymath}
D_{\perp 2}-D_{\perp 1} = 0,
\end{displaymath}">|; 

$key = q/displaystylefrac{Q}{Q_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="$\displaystyle \frac{Q}{Q_0}$">|; 

$key = q/sigmasimeq5,(Omega,{{rm{m})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2417.png"
 ALT="$\sigma\simeq 5 (\Omega {\rm m})^{-1}$">|; 

$key = q/u<c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2761.png"
 ALT="$u&lt;c$">|; 

$key = q/RllR_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="$R\ll R_0$">|; 

$key = q/displaystyleB_{parallel,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2463.png"
 ALT="$\displaystyle B_{\parallel 1}$">|; 

$key = q/{displaymath}U=frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3216.png"
 ALT="\begin{displaymath}
U = \frac{\epsilon_0  E^2}{2} + \frac{B^2}{2 \mu_0},
\end{displaymath}">|; 

$key = q/partial^2Gslashpartialz^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="$\partial^2 G/\partial z^2$">|; 

$key = q/{displaymath}sigma=frac{omega^4}{(omega^2-omega_0^{,2})^2},sigma_T,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2304.png"
 ALT="\begin{displaymath}
\sigma = \frac{\omega^4}{(\omega^2-\omega_0^{ 2})^2} \sigma_T,
\end{displaymath}">|; 

$key = q/z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1695.png"
 ALT="$z=0$">|; 

$key = q/hat{{bf{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2604.png"
 ALT="$\hat{\bf n}$">|; 

$key = q/{displaymath}E_z(x,t)=intF(k),{{rm{e}^{,{{rm{i},phi(k)},dk,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img2335.png"
 ALT="\begin{displaymath}
E_z(x,t) = \int F(k) {\rm e}^{ {\rm i} \phi(k)} dk,
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{plane.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img1704.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{plane.eps}}
\end{figure}">|; 

$key = q/costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$\cos\theta$">|; 

$key = q/dS_{4'}=d^{3}x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3293.png"
 ALT="$dS_{4'} = d^{3}x'$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}intfrac{left[rho({{bf{r'})right]}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \frac{1}{4\pi \epsilon_0} \int\frac{\left[\...
...{\bf r'})\right]}
{\vert{\bf r} - {\bf r'}\vert} 
d^3{\bf r'}
\end{displaymath}">|; 

$key = q/H_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1834.png"
 ALT="$H_c$">|; 

$key = q/{displaymath}-frac{partial}{partialt}int_Vg_i,dV=int_SG_{ij},dS_j+int_Vleft[rho,{{bf{E}+{{bf{j}times{{bf{B}right]_i,dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2168.png"
 ALT="\begin{displaymath}
-\frac{\partial}{\partial t}\int_V g_i dV = \int_S G_{ij} ...
...int_V \left[\rho {\bf E} + {\bf j}\times{\bf B}\right]_i dV.
\end{displaymath}">|; 

$key = q/{displaymath}-{{bf{E}cdot{{bf{j}=-frac{{{bf{E}cdotnablatimes{{bf{B}}{mu_0}+frac{al}{partialt}!left(frac{epsilon_0,E^2}{2}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2118.png"
 ALT="\begin{displaymath}
- {\bf E} \cdot {\bf j} = - \frac{ {\bf E}\cdot \nabla\times...
...partial}{\partial t}\!\left(\frac{\epsilon_0  E^2}{2}\right).
\end{displaymath}">|; 

$key = q/{displaymath}beta^2=frac{cos^2theta_t}{cos^2theta_i}=frac{1-sin^2theta_t}{1-sin^frac{1-sin^2theta_islashbeta^2}{1-sin^2theta_i},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2567.png"
 ALT="\begin{displaymath}
\beta^2 = \frac{\cos^2\theta_t}{\cos^2\theta_i} = \frac{1-\s...
...^2\theta_i}=\frac{1-\sin^2\theta_i/\beta^2}{1-\sin^2\theta_i},
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2left(frac{1}{|{{bf{r}-{{bf{r}'|}right)=-4pi,delta({{bf{r}-{{bf{r}').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="\begin{displaymath}
\nabla^2 \left(\frac{1}{\vert{\bf r} - {\bf r}'\vert} \right)= - 4\pi \delta({\bf r} - {\bf r}').
\end{displaymath}">|; 

$key = q/{{bf{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="${\bf k}$">|; 

$key = q/displaystyle|a|^2,|b|^2-({{bf{a}cdot{{bf{b})^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \vert a\vert^2  \vert b\vert^2 - ({\bf a}\cdot {\bf b})^2$">|; 

$key = q/{displaymath}nablacdot{{bf{E}=frac{q}{epsilon_0},delta({{bf{r}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf E} = \frac{q}{\epsilon_0}  \delta({\bf r}),
\end{displaymath}">|; 

$key = q/a,bsintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$a b \sin\theta$">|; 

$key = q/{displaymath}I_1=frac{V_1}{R_1}left[1-exp(-R_1,tslashL_1),right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1931.png"
 ALT="\begin{displaymath}
I_1 = \frac{V_1}{R_1} \left[ 1 - \exp(-R_1  t/L_1) \right].
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intleft([rho],frac{{bf{R}{R^3}+left[frac{parti}{c,R^2}-frac{[partial{{bf{j}slashpartialt]}{c^2,R}right)dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="$\displaystyle \frac{1}{4\pi \epsilon_0} \int \left(
[\rho]  \frac{\bf R}{R^3}...
...frac{\bf R}{c R^2}
- \frac{[\partial {\bf j}/\partial t]}{c^2  R} \right)dV',$">|; 

$key = q/displaystylefrac{mu_0,e}{4pi}frac{{bf{u}{s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3235.png"
 ALT="$\displaystyle \frac{\mu_0 e}{4\pi} \frac{\bf u}{s},$">|; 

$key = q/{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="${\bf A}\cdot d{\bf S}$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right){{bf{B}={{bf{0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="\begin{displaymath}
\left( \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}\right) {\bf B} = {\bf0},
\end{displaymath}">|; 

$key = q/{bf{v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\bf v$">|; 

$key = q/omega=1slashsqrt{L,C}pmRslash2,L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2032.png"
 ALT="$\omega = 1/\sqrt{L C} \pm R/2 L$">|; 

$key = q/{displaymath}{{bf{B}rightarrow{{bf{B}~~~{{rm{as}~~~{{bf{A}rightarrow{{bf{A}+nablapsi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="\begin{displaymath}
{\bf B} \rightarrow {\bf B}&nbsp;&nbsp;&nbsp;{\rm as}&nbsp;&nbsp;&nbsp;{\bf A} \rightarrow {\bf A} + \nabla\psi.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial}{partialz}!left(frac{1}{R_1}right)_{z=0}=-frac{partial}{R_2}right)_{z=0}=frac{d}{(r^2+d^2)^{3slash2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1717.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial z}\!\left(\frac{1}{R_1}\right)_{z=0...
...!\left(\frac{1}{R_2}\right)_{z=0}
= \frac{d}{(r^2+d^2)^{3/2}}.
\end{displaymath}">|; 

$key = q/n=1,2,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2632.png"
 ALT="$n=1, 2, \cdots$">|; 

$key = q/displaystylefrac{d^2X}{dx^2}=~k^2,X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1614.png"
 ALT="$\displaystyle \frac{d^2 X}{d x^2} =&nbsp; k^2 X,$">|; 

$key = q/{mitOmega}=q,Bslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="${\mit\Omega} = q B/m$">|; 

$key = q/Q=(4slash3)pi,a^3,rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="$Q = (4/3)\pi  a^3  \rho$">|; 

$key = q/{bf{a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\bf a$">|; 

$key = q/{displaymath}(nablatimes{{bf{B})_z=mu_0,j_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf B})_z = \mu_0  j_z.
\end{displaymath}">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{[{{bf{j}]}{R},dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \frac{[{\bf j}]}{R}  dV',$">|; 

$key = q/{{bf{j}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1774.png"
 ALT="${\bf j}_t$">|; 

$key = q/{displaymath}nablacdot({{bf{A}times{{bf{B})equiv{{bf{B}cdotnablatimes{{bf{A}-{{bf{A}cdotnablatimes{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1997.png"
 ALT="\begin{displaymath}
\nabla\cdot({\bf A} \times{\bf B}) \equiv {\bf B} \cdot \nabla\times{\bf A} -
{\bf A} \cdot \nabla\times{\bf B},
\end{displaymath}">|; 

$key = q/{{bf{E}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="${\bf E}({\bf r})$">|; 

$key = q/I=n,q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1945.png"
 ALT="$I=n q$">|; 

$key = q/({x^i}',t');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3227.png"
 ALT="$({x^i}', t')$">|; 

$key = q/<10^{-11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="$&lt;10^{-11}$">|; 

$key = q/{displaymath}p=frac{epsilon_0,E^2}{2}=,langleUrangle.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2158.png"
 ALT="\begin{displaymath}
p = \frac{\epsilon_0 E^2}{2} =  \langle U\rangle.
\end{displaymath}">|; 

$key = q/E_3^{~2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1451.png"
 ALT="$E_3^{&nbsp;2}$">|; 

$key = q/(dTslashdl)_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$(dT/dl)_{\rm max}$">|; 

$key = q/{{bf{A}_1={{bf{A}_2={{bf{A}_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1457.png"
 ALT="${\bf A}_1={\bf A}_2={\bf A}_S$">|; 

$key = q/{displaymath}mfrac{d{{bf{v}}{dt}=q,{{bf{E}+q,{{bf{v}times{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="\begin{displaymath}
m\frac{d{\bf v}}{dt} = q {\bf E} + q {\bf v} \times{\bf B},
\end{displaymath}">|; 

$key = q/{displaymath}C=frac{q}{V}=frac{2pi,epsilon_0}{lnbslasha}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1394.png"
 ALT="\begin{displaymath}
C = \frac{q}{V} = \frac{2\pi \epsilon_0}{\ln b/a}.
\end{displaymath}">|; 

$key = q/D_perp=epsilon_0,epsilon,E_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1732.png"
 ALT="$D_\perp=\epsilon_0 \epsilon E_\perp$">|; 

$key = q/{{bf{R_ast}={{bf{r}-{{bf{r}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="${\bf R_\ast} = {\bf r} - {\bf r}_\ast$">|; 

$key = q/displaystyleE_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1742.png"
 ALT="$\displaystyle E_1$">|; 

$key = q/lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2095.png"
 ALT="$\lambda/2$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig17.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="230" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig17.eps}}
\end{figure}">|; 

$key = q/u_r=u,xslashr={{bf{r}!cdot!{{bf{u}slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3121.png"
 ALT="$u_r = u x/r = {\bf r}\!\cdot\!{\bf u}/r$">|; 

$key = q/U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="$U$">|; 

$key = q/{displaymath}P_{{rm{load}=frac{E_0^{,2},l^2}{8,R_{{rm{rad}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2256.png"
 ALT="\begin{displaymath}
P_{\rm load} = \frac{E_0^{ 2}  l^2}{8  R_{\rm rad}}.
\end{displaymath}">|; 

$key = q/displaystyledx'^2+dy'^2+dz'^2-c^2,dt'^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2671.png"
 ALT="$\displaystyle dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2$">|; 

$key = q/{displaymath}(nablatimes{{bf{A})_theta=frac{1}{r,sintheta}frac{partialA_r}{partialphi}-frac{1}{r}frac{partial(rA_phi)}{partialr}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf A})_\theta =
\frac{1}{r \sin\theta}\frac...
...artial \phi}-\frac{1}{r}\frac{\partial (r A_\phi)}{\partial r}
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j}+epsilon_0mu_0frac{partial{{bf{E}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2116.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0  {\bf j} +\epsilon_0\mu_0 \frac{\partial {\bf E}}
{\partial t}.
\end{displaymath}">|; 

$key = q/(x_1,y_1,z_1,t_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2856.png"
 ALT="$(x_1, y_1, z_1, t_1)$">|; 

$key = q/{displaymath}{{bf{A}rightarrow{{bf{A}-nablapsi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="\begin{displaymath}
{\bf A} \rightarrow {\bf A} - \nabla\psi.
\end{displaymath}">|; 

$key = q/{displaymath}P_{{rm{rad}=oint_Slangle{{bf{u}ranglecdotd{{bf{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img2228.png"
 ALT="\begin{displaymath}
P_{\rm rad} = \oint_S \langle {\bf u}\rangle\cdot d{\bf S},
\end{displaymath}">|; 

$key = q/{displaymath}[rho]simeqrho-frac{partialrho}{partialt}frac{R}{c}+frac{1}{2}frac{partial^2rho}{partialt^2}frac{R^2}{c^2}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="\begin{displaymath}[\rho]\simeq \rho - \frac{\partial \rho}{\partial t} \frac{R}...
...\frac{\partial^2 \rho}{\partial t^2} \frac{R^2}{c^2} + \cdots.
\end{displaymath}">|; 

$key = q/{displaymath}g_{mu'sigma'},g^{nu'sigma'},p_{musigma}^{mu'}=p_{musigma}^{nu'}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2929.png"
 ALT="\begin{displaymath}
g_{\mu'\sigma'} g^{\nu'\sigma'} p_{\mu\sigma}^{\mu'} = p_{\mu\sigma}^{\nu'}
=0.
\end{displaymath}">|; 

$key = q/displaystylez'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$\displaystyle z'.$">|; 

$key = q/nabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$\nabla$">|; 

$key = q/{displaymath}DeltaW=intoint{{bf{H}!cdotd{{bf{B},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1860.png"
 ALT="\begin{displaymath}
\Delta W = \int \oint {\bf H}\!\cdot d{\bf B}  d^3{\bf r}.
\end{displaymath}">|; 

$key = q/{displaymath}R=frac{V(l,t)}{I(l,t)}=sqrt{frac{L}{C}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img2062.png"
 ALT="\begin{displaymath}
R = \frac{V(l, t)}{I(l, t)} = \sqrt{\frac{L}{C}}.
\end{displaymath}">|; 

$key = q/displaystylephi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1403.png"
 ALT="$\displaystyle \phi_1$">|; 

$key = q/{{bf{P}({{bf{r})=N({{bf{r}),q,{{bf{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1666.png"
 ALT="${\bf P}({\bf r}) = N({\bf r}) q {\bf d}$">|; 

$key = q/dq=-N(x+dx,y,z),q,d_x,dy,dz+N(x,y,z),q,d_x,dy,dz=-[partialN(x,y,z)slashpartialx],q,d_x,dx,dy,dz=-[partialP_x(x,y,z)slashpartialx],dx,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="956" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1669.png"
 ALT="$dq = -N(x+dx,y,z) q d_x dy dz + N(x,y,z) q d_x dy dz =
- [\partial N(x...
...artial x] q d_x dx dy dz = - [\partial P_x(x,y,z)/\partial x] 
dx dy dz$">|; 

$key = q/{displaymath}V=phi(oplus)-phi(ominus)=-int_{oplus}^{ominus}nablaphicdotd{{bf{l}=int_{oplus}^{ominus}{{bf{E}cdotd{{bf{l},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="\begin{displaymath}
V = \phi(\oplus)-\phi(\ominus) =
-\int_{\oplus}^{\ominus} \n...
...dot
d{\bf l} = \int_{\oplus}^{\ominus} {\bf E} \cdot d{\bf l},
\end{displaymath}">|; 

$key = q/dfslashdx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$df/dx$">|; 

$key = q/{displaymath}({{bf{b}-{{bf{a})cdot({{bf{b}-{{bf{a})=|a|^2+|b|^2-2,{{bf{a}cdot{{bf{b}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="\begin{displaymath}
({\bf b} - {\bf a} ) \cdot ({\bf b} - {\bf a} ) = \vert a\vert^2 + \vert b\vert^2 - 2 {\bf a} \cdot
{\bf b}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{sigma}{2epsilon_0}mbox{hspace{2cm}below}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="$\displaystyle -\frac{\sigma}{2\epsilon_0} \mbox{\hspace{2cm} below}.$">|; 

$key = q/{displaymath}-frac{partial}{partialt}left[epsilon_0,{{bf{E}times{{bf{B}right]_i=partialx_j}+[rho,{{bf{E}+{{bf{j}times{{bf{B}]_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2175.png"
 ALT="\begin{displaymath}
-\frac{\partial}{\partial t}\left[\epsilon_0 {\bf E}\times{...
...ij}}{\partial x_j} + [\rho {\bf E} + {\bf j}\times{\bf B}]_i.
\end{displaymath}">|; 

$key = q/n_esim10^3slashm_psim10^{30},{{rm{m}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2290.png"
 ALT="$n_e \sim 10^3/m_p\sim 10^{30} {\rm m}^{-3}$">|; 

$key = q/n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2445.png"
 ALT="$n_2$">|; 

$key = q/{displaymath}phi(x,y)rightarrow0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1604.png"
 ALT="\begin{displaymath}
\phi(x, y)\rightarrow 0
\end{displaymath}">|; 

$key = q/{displaymath}frac{E_i-E_r}{v_1}=frac{E_t}{v_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2553.png"
 ALT="\begin{displaymath}
\frac{E_i-E_r}{v_1} = \frac{E_t}{v_2}.
\end{displaymath}">|; 

$key = q/{displaymath}phi(Q)=phi(P)+int_P^Qnablaphicdotd{{bf{l}=phi(P)+int_P^Q{{bf{A}cdotd{{bf{l},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="\begin{displaymath}
\phi(Q) = \phi(P)+\int_P^Q \nabla\phi\cdot d{\bf l} =
\phi(P)+\int_P^Q {\bf A}\cdot d{\bf l},
\end{displaymath}">|; 

$key = q/I=I_0,cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2234.png"
 ALT="$I= I_0  \cos(\omega  t)$">|; 

$key = q/{displaymath}P_{{rm{load}=langleu_{{rm{in}rangleA_{{rm{eff}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2258.png"
 ALT="\begin{displaymath}
P_{\rm load} = \langle u_{\rm in}\rangle A_{\rm eff}.
\end{displaymath}">|; 

$key = q/displaystylephi(x^i,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3236.png"
 ALT="$\displaystyle \phi(x^i, t)$">|; 

$key = q/displaystyle{{bf{E}_{{rm{analogue}(z>0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1512.png"
 ALT="$\displaystyle {\bf E}_{\rm analogue}(z&gt;0),$">|; 

$key = q/m_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3148.png"
 ALT="$m_0$">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0,c^2}frac{sintheta}{r},dot{u},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3279.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0  c^2} \frac{\sin\theta}{r}  \dot{u},$">|; 

$key = q/int_V{nabla}cdot{{bf{E},dV=qslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="$\int_V {\nabla}\cdot {\bf E}  dV= q/\epsilon_0$">|; 

$key = q/stackrel{displaystylerightarrow}{PQ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PQ}$">|; 

$key = q/nablatimes{{bf{H}={{bf{j}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1848.png"
 ALT="$\nabla\times{\bf H}
= {\bf j}_t$">|; 

$key = q/{displaymath}W=frac{1}{2}sum_{i=1}^NI_i,{mitPhi}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1989.png"
 ALT="\begin{displaymath}
W= \frac{1}{2} \sum_{i=1}^N I_i  {\mit\Phi}_i.
\end{displaymath}">|; 

$key = q/{displaymath}dot{{bf{u}!cdot!{{bf{r}=-dot{u},r,sinalpha,sinphi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img3366.png"
 ALT="\begin{displaymath}
\dot{\bf u}\!\cdot\!{\bf r} = -\dot{u}  r  \sin\alpha \sin\phi.
\end{displaymath}">|; 

$key = q/rggl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2211.png"
 ALT="$r\gg l$">|; 

$key = q/n_1=n_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2476.png"
 ALT="$n_1=n_2$">|; 

$key = q/{displaymath}g_{mu'nu'},p_{musigma}^{mu'},p_{nu}^{nu'},p_{sigma'}^{nu}=g_{mu'sigma'},p_{musigma}^{mu'}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2927.png"
 ALT="\begin{displaymath}
g_{\mu'\nu'}  p_{\mu\sigma}^{\mu'}  p_{\nu}^{\nu'} p_{\sigma'}^{\nu}
= g_{\mu'\sigma'} p_{\mu\sigma}^{\mu'} =0.
\end{displaymath}">|; 

$key = q/{{bf{E}({{bf{r}_i)={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="${\bf E}({\bf r}_i)={\bf0}$">|; 

$key = q/displaystyleepsilon_0mu_0,frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle \epsilon_0\mu_0 \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/{displaymath}{{bf{F}=-frac{1}{4pi,epsilon_0}frac{q^2}{(2,d)^2},hat{{bf{z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1506.png"
 ALT="\begin{displaymath}
{\bf F} = - \frac{1}{4\pi \epsilon_0} \frac{q^2}{(2 d)^2}  \hat{\bf z}.
\end{displaymath}">|; 

$key = q/R_2=sqrt{r^2+(d+z)^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1708.png"
 ALT="$R_2= \sqrt{r^2+(d+z)^2}$">|; 

$key = q/nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2427.png"
 ALT="$\nu$">|; 

$key = q/y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$y'$">|; 

$key = q/displaystylefrac{epsilon_0,E_0^{,2}}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2150.png"
 ALT="$\displaystyle \frac{\epsilon_0  E_0^{ 2}}{2},$">|; 

$key = q/{displaymath}alpha=frac{partialh}{partialx},~~~~~beta=frac{partialh}{partialy},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="\begin{displaymath}
\alpha = \frac{\partial h}{\partial x},&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\beta= \frac{\partial h}{\partial y},
\end{displaymath}">|; 

$key = q/displaystyle{{bf{0}mbox{hspace{3.9cm}otherwise}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="$\displaystyle {\bf0} \mbox{\hspace{3.9cm} otherwise}.$">|; 

$key = q/{displaymath}B_0-B_0,alpha=(mu_0slashmu),B_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1824.png"
 ALT="\begin{displaymath}
B_0 - B_0 \alpha = (\mu_0/\mu) B_1.
\end{displaymath}">|; 

$key = q/f_n(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1642.png"
 ALT="$f_n(x)$">|; 

$key = q/R_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1919.png"
 ALT="$R_2$">|; 

$key = q/{displaymath}nablatimesnablaphi=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="\begin{displaymath}
\nabla\times\nabla\phi = 0
\end{displaymath}">|; 

$key = q/{displaymath}Q=-frac{q,d}{2}int_0^inftyfrac{dk}{(k+d^2)^{3slash2}}=q,dleft[frac{1}{(k+d^2)^{1slash2}}right]_0^infty=-q.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img1504.png"
 ALT="\begin{displaymath}
Q = - \frac{q d}{2} \int_0^\infty \frac{dk}{(k+d^2)^{3/2}}
= q d\left[ \frac{1}{(k+d^2)^{1/2}}\right]_0^\infty = - q.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig32.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="286" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig32.eps}}
\end{figure}">|; 

$key = q/y+dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1663.png"
 ALT="$y+dy$">|; 

$key = q/displaystyleepsilon^{ijk},epsilon_{ijb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3008.png"
 ALT="$\displaystyle \epsilon^{ijk} \epsilon_{ijb}$">|; 

$key = q/t=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="$t=0.1$">|; 

$key = q/{displaymath}nabla^2U=-D.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="\begin{displaymath}
\nabla^2 U = -D.
\end{displaymath}">|; 

$key = q/{displaymath}W=int_{{rm{all,space}frac{B^2}{2,mu_0},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2002.png"
 ALT="\begin{displaymath}
W = \int_{\rm all space} \frac{B^2}{2 \mu_0}   dV.
\end{displaymath}">|; 

$key = q/displaystyleleft(sintheta_t,,0,,costheta_tright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2521.png"
 ALT="$\displaystyle \left(\sin\theta_t, 0, \cos\theta_t\right).$">|; 

$key = q/{displaymath}(nablatimes{{bf{B})_x=mu_0,j_x,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf B})_x = \mu_0  j_x,
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig22.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig22.eps}}
\end{figure}">|; 

$key = q/{displaymath}phi({{bf{r})=sum_{i=1}^Nphi_i({{bf{r}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \sum_{i=1}^N \phi_i ({\bf r}),
\end{displaymath}">|; 

$key = q/{{bf{r}=({{bf{k}slashk),r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="${\bf r} = ({\bf k} /k) r$">|; 

$key = q/displaystylefrac{e}{4piepsilon_0}frac{1}{s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3237.png"
 ALT="$\displaystyle \frac{e}{4\pi\epsilon_0} \frac{1}{s},$">|; 

$key = q/{displaymath}F(phi)=-frac{delta(phi)}{4pi}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="\begin{displaymath}
F(\phi) = -\frac{\delta(\phi)}{4\pi}.
\end{displaymath}">|; 

$key = q/displaystylenablacdot{{bf{E}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1426.png"
 ALT="$\displaystyle \nabla\cdot{\bf E}_1$">|; 

$key = q/d{{bf{S}=(dS_x,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$d{\bf S} = (dS_x, 0, 0)$">|; 

$key = q/{displaymath}sigma_b=epsilon_0,(E_{z,1}-E_{z,2})_{z=0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1725.png"
 ALT="\begin{displaymath}
\sigma_b = \epsilon_0 (E_{z 1}-E_{z 2})_{z=0}.
\end{displaymath}">|; 

$key = q/u=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2763.png"
 ALT="$u=c$">|; 

$key = q/{{bf{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="${\bf W}$">|; 

$key = q/displaystyleC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2715.png"
 ALT="$\displaystyle C$">|; 

$key = q/dW=p,A,dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="$dW = p A dx$">|; 

$key = q/v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="$v_2$">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle {\bf a}\cdot {\bf a}\times{\bf b}$">|; 

$key = q/z=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1518.png"
 ALT="$z=\infty$">|; 

$key = q/{displaymath}{{bf{P}=epsilon_0,(epsilon-1),{{bf{E}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2309.png"
 ALT="\begin{displaymath}
{\bf P} = \epsilon_0 (\epsilon -1) {\bf E}.
\end{displaymath}">|; 

$key = q/{displaymath}{{rm{i},{{bf{k}cdot{{bf{B}_0=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="\begin{displaymath}
{\rm i} {\bf k} \cdot {\bf B}_0 = 0,
\end{displaymath}">|; 

$key = q/v_1+v_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$v_1 + v_2$">|; 

$key = q/{displaymath}oint_S{{bf{A}cdotd{{bf{S}=int_V{mitdiv},{{bf{A},,dV{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="\begin{displaymath}
\oint_S {\bf A}\cdot d{\bf S} = \int_V {\mit div} {\bf A}  dV
\end{displaymath}">|; 

$key = q/{{bf{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="${\bf H}$">|; 

$key = q/displaystyle{{bf{0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$\displaystyle {\bf0},$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}frac{q'}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="\begin{displaymath}
\phi({\bf r})= \frac{1}{4\pi \epsilon_0} \frac{q'}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig43.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="650" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig43.eps}}
\end{figure}">|; 

$key = q/E_1>E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1751.png"
 ALT="$E_1 &gt; E_0$">|; 

$key = q/{displaymath}L=mu_0,N^2,pi,r^2,l,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1971.png"
 ALT="\begin{displaymath}
L = \mu_0  N^2 \pi  r^2  l,
\end{displaymath}">|; 

$key = q/-v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2727.png"
 ALT="$-v$">|; 

$key = q/{displaymath}V=oint{{bf{E}cdotd{{bf{l}neq0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="\begin{displaymath}
V = \oint{\bf E} \cdot d{\bf l} \neq 0,
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_0cos,({{bf{k}cdot{{bf{r}-omega,t+phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="$\displaystyle {\bf B}_0 \cos ({\bf k}\cdot {\bf r} - \omega  t+\phi).$">|; 

$key = q/{displaymath}m_e,omega^2,s_{pm}=e,(E_{pm}mpomega,B_0,s_pm),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2362.png"
 ALT="\begin{displaymath}
m_e \omega^2 s_{\pm} = e (E_{\pm} \mp \omega B_0 s_\pm),
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=-nablaphi,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="\begin{displaymath}
{\bf E} = -\nabla \phi,
\end{displaymath}">|; 

$key = q/partial_muJ^{mu}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3054.png"
 ALT="$\partial_\mu J^{\mu} =0$">|; 

$key = q/{{bf{a}=(a_x,,a_y,,a_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="${\bf a} = (a_x,  a_y,  a_z)$">|; 

$key = q/{{bf{C};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="${\bf C} $">|; 

$key = q/displaystyleleft(frac{3(x-x')^2-|{{bf{r}-{{bf{r}'|^2}{|{{bf{r}-{{bf{r}'|^5}right)F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="$\displaystyle \left(\frac{3(x-x')^2 - \vert{\bf r} - {\bf r}'\vert^2}
{\vert{\bf r} - {\bf r}'\vert^5 } \right) F$">|; 

$key = q/{displaymath}frac{dsigma}{d{mitOmega}}=frac{omega^4}{(omega^2-omega_0^{,2})^2},r_e^{,2},sin^2theta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2303.png"
 ALT="\begin{displaymath}
\frac{d\sigma}{d{\mit\Omega}} = \frac{\omega^4}{(\omega^2-\omega_0^{ 2})^2} r_e^{ 2} \sin^2\theta,
\end{displaymath}">|; 

$key = q/displaystyle-F^{4i}=+E^i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3043.png"
 ALT="$\displaystyle -F^{4i} = +E^i,$">|; 

$key = q/{displaymath}E^i=frac{1}{2},epsilon^{ijk}E_{jk}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3056.png"
 ALT="\begin{displaymath}
E^i =\frac{1}{2} \epsilon^{ijk} E_{jk}.
\end{displaymath}">|; 

$key = q/C_{kl}^j=A^{ij}B_{ikl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2811.png"
 ALT="$C_{kl}^j = A^{ij} B_{ikl}$">|; 

$key = q/{{bf{a}times{{bf{a}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="${\bf a}\times{\bf a} = {\bf0}$">|; 

$key = q/{displaymath}W=intint_0^Efrac{epsilon_0,epsilon,delta(E^2)}{2},d^3{{bf{r}=frac{1}{2}intepsilon_0,epsilon,E^2,d^{3}{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1763.png"
 ALT="\begin{displaymath}
W = \int \int_0^E \frac{\epsilon_0 \epsilon  \delta (E^2)}...
...
= \frac{1}{2} \int \epsilon_0 \epsilon  E^2 d^{3} {\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}P_{{rm{rad}=langleI^2R_{{rm{rad}rangle=frac{R_{{rm{rad},V_0^{,2}}{2,(R_{{rm{rad}+R_{{rm{load})^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2249.png"
 ALT="\begin{displaymath}
P_{\rm rad} = \langle I^2 R_{\rm rad}\rangle = \frac{R_{\rm rad}  V_0^{ 2}}
{2 (R_{\rm rad} + R_{\rm load})^2}.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{E}=rhoslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="$\nabla\cdot {\bf E} = \rho/\epsilon_0$">|; 

$key = q/displaystylenabla^2phi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1401.png"
 ALT="$\displaystyle \nabla^2 \phi_2$">|; 

$key = q/dz'=dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2744.png"
 ALT="$dz'=dz$">|; 

$key = q/{displaymath}frac{Q}{Q'}simeqfrac{a}{b}gg1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1382.png"
 ALT="\begin{displaymath}
\frac{Q}{Q'} \simeq \frac{a}{b} \gg 1.
\end{displaymath}">|; 

$key = q/{displaymath}sigma=epsilon_0,E_r(r=a)=-epsilon_0,frac{partialphi(r=a)}{partialr}=3,epsilon_0,E_0,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="401" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1654.png"
 ALT="\begin{displaymath}
\sigma = \epsilon_0 E_r(r=a) = -\epsilon_0 \frac{\partial \phi(r=a)}{\partial r} = 3 \epsilon_0 E_0 \cos\theta.
\end{displaymath}">|; 

$key = q/{displaymath}f_i=e,(E_i+epsilon_{ijk},u^jB^k),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3171.png"
 ALT="\begin{displaymath}
f_i = e (E_i + \epsilon_{ijk}  u^j B^k),
\end{displaymath}">|; 

$key = q/10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="$10^{-4}$">|; 

$key = q/{displaymath}F^{munu}=frac{e}{4pi,epsilon_0,c,{r'}^3},U^muR^nu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img3130.png"
 ALT="\begin{displaymath}
F^{\mu\nu} = \frac{e}{4\pi \epsilon_0 c {r'}^3} U^\mu R^\nu.
\end{displaymath}">|; 

$key = q/B_z(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2621.png"
 ALT="$B_z(x,y)$">|; 

$key = q/epsilon>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1746.png"
 ALT="$\epsilon&gt;1$">|; 

$key = q/-0.21times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1791.png"
 ALT="$-0.21\times 10^{-8}$">|; 

$key = q/displaystyleR_1,I_1+L,frac{dI_1}{dt}+M,frac{dI_2}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1956.png"
 ALT="$\displaystyle R_1  I_1 + L \frac{d I_1}{dt} +M \frac{d I_2}{dt},$">|; 

$key = q/{displaymath}{{bf{k}times({{bf{k}times{{bf{E}_0)=({{bf{k}cdot{{bf{E}_0),{{bf{k}-=k^2,{{bf{E}_0=-epsilon_0mu_0,omega^2,{{bf{E}_0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="\begin{displaymath}
{\bf k}\times ({\bf k} \times {\bf E}_0) =
({\bf k} \cdot {...
..._0 =k^2 {\bf E}_0
= - \epsilon_0 \mu_0 \omega^2  {\bf E}_0,
\end{displaymath}">|; 

$key = q/{displaymath}W=int_{{bf{0}^{{bf{D}deltaW=int_{{bf{0}^{{bf{D}int{{bf{E}!cdot!delta{{bf{D},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1762.png"
 ALT="\begin{displaymath}
W = \int_{\bf0}^{\bf D} \delta W = \int_{\bf0}^{\bf D }\int {\bf E}\!\cdot\!
\delta{\bf D} d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}W=sum_{i=1}^Nint_0^TI_{0,i},{mitPhi}_{0,i},frac{t}{T^2},dt,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1986.png"
 ALT="\begin{displaymath}
W = \sum_{i=1}^N \int_0^T I_{0 i}  {\mit\Phi}_{0 i}  \frac{t}{T^2} dt,
\end{displaymath}">|; 

$key = q/alpha_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\alpha_x$">|; 

$key = q/U^mu=gamma,({{bf{u},c);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3174.png"
 ALT="$U^\mu = \gamma ({\bf u}, c)$">|; 

$key = q/(pm1,0,0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2675.png"
 ALT="$(\pm 1, 0, 0, 1)$">|; 

$key = q/{mitPhi}=L,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1890.png"
 ALT="${\mit\Phi} = L  I$">|; 

$key = q/{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="${\bf S}$">|; 

$key = q/displaystylefrac{rho}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="$\displaystyle \frac{\rho}{\epsilon_0},$">|; 

$key = q/{displaymath}oint_{S'}{{bf{B}cdotd{{bf{S}'=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="\begin{displaymath}
\oint_{S'} {\bf B} \cdot d{\bf S}' = 0,
\end{displaymath}">|; 

$key = q/({{bf{r}-{{bf{r'})slash{|{{bf{r}-{{bf{r'}|^3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="$({\bf r} - {\bf r'})/{\vert{\bf r} - {\bf r'}\vert^3}$">|; 

$key = q/{displaymath}x^2-c^2,t^2=x'^2-c^2,t'^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img2705.png"
 ALT="\begin{displaymath}
x^2 - c^2  t^2 = x'^2 - c^2  t'^2.
\end{displaymath}">|; 

$key = q/displaystylehat{{bf{k}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2518.png"
 ALT="$\displaystyle \hat{\bf k}_r$">|; 

$key = q/{{bf{a}+{{bf{b}={{bf{b}+{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="${\bf a} + {\bf b} = {\bf b}+{\bf a}$">|; 

$key = q/displaystylenablacdot{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="$\displaystyle \nabla\cdot{\bf B}$">|; 

$key = q/R_mu,Q^mu=-{{bf{r}!cdot!{{bf{q}+c,t,k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2902.png"
 ALT="$ R_\mu  Q^\mu = - {\bf r}\!\cdot\!{\bf q} + c t k$">|; 

$key = q/{{rm{i},{{bf{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="${\rm i} {\bf k}$">|; 

$key = q/displaystylez',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2724.png"
 ALT="$\displaystyle z',$">|; 

$key = q/{displaymath}rho=rho_f+rho_b.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1676.png"
 ALT="\begin{displaymath}
\rho = \rho_f + \rho_b.
\end{displaymath}">|; 

$key = q/{displaymath}[{{bf{r}times({{bf{r}_utimesdot{{bf{u})]^2=dot{u}^2,r^4left[left(1-1-frac{u^2}{c^2}right)tan^2phi,cos^2thetaright].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3368.png"
 ALT="\begin{displaymath}[{\bf r}\times({\bf r}_u\times \dot{\bf u})]^2 =
\dot{u}^2  ...
...t(
1-\frac{u^2}{c^2}\right) \tan^2 \phi  \cos^2\theta\right].
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig26.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig26.eps}}
\end{figure}">|; 

$key = q/displaystyleE_parallel';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3093.png"
 ALT="$\displaystyle E_\parallel'$">|; 

$key = q/displaystyle{T^i}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3198.png"
 ALT="$\displaystyle {T^i}_j$">|; 

$key = q/{displaymath}U_muA^mu=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2950.png"
 ALT="\begin{displaymath}
U_\mu A^\mu = 0
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2{{bf{A}=-mu_0,{{bf{j}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="\begin{displaymath}
\nabla^2{\bf A} = - \mu_0  {\bf j}.
\end{displaymath}">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$P$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="$q$">|; 

$key = q/oint{{bf{A}cdotd{{bf{l}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$\oint {\bf A}\cdot d{\bf l} \neq 0$">|; 

$key = q/{displaymath}frac{1}{X}frac{d^2X}{dx^2}=k^2=-frac{1}{Y}frac{d^2Y}{dy^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1611.png"
 ALT="\begin{displaymath}
\frac{1}{X}\frac{d^2 X}{d x^2} = k^2 =- \frac{1}{Y} \frac{d^2 Y}{d y^2}.
\end{displaymath}">|; 

$key = q/{displaymath}s=r_0,sqrt{1-u^2slashc^2+u_r^{~2}slashc^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img3267.png"
 ALT="\begin{displaymath}
s = r_0 \sqrt{1-u^2/c^2 + u_r^{&nbsp;2}/c^2}
\end{displaymath}">|; 

$key = q/int_{S_2}{{bf{j}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="$\int_{S_2} {\bf j}
\cdot d{\bf S} $">|; 

$key = q/dy'=dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2743.png"
 ALT="$dy'=dy$">|; 

$key = q/displaystylefrac{q}{4pi,epsilon_0}frac{1}{|{{bf{r}-{{bf{r}_0|}mbox{hspace{1cm}for,{t_1leqt-|{{bf{r}-{{bf{r}_0|slashcleqt_2{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="$\displaystyle \frac{q}{4\pi  \epsilon_0} \frac{1}{\vert{\bf r} - {\bf r}_0\vert}
\mbox{\hspace{1cm} for  $ t_1\leq t-\vert{\bf r} - {\bf r}_0\vert/c \leq t_2$}$">|; 

$key = q/{displaymath}P(t')=frac{e^2}{6pi,epsilon_0,c^3},gamma^6,dot{u}^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3354.png"
 ALT="\begin{displaymath}
P(t') = \frac{e^2}{6\pi \epsilon_0  c^3} \gamma^6 \dot{u}^2,
\end{displaymath}">|; 

$key = q/0.26,lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2262.png"
 ALT="$0.26 \lambda$">|; 

$key = q/displaystylefrac{epsilon_0,E_0^{,2}}{2,c},hat{{bf{k}=frac{langleUrangle}{c},hat{{bf{k},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2154.png"
 ALT="$\displaystyle \frac{\epsilon_0  E_0^{ 2}}{2 c} \hat{\bf k} = \frac{\langle U\rangle}{c}
 \hat{\bf k},$">|; 

$key = q/epsilon=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2438.png"
 ALT="$\epsilon=1$">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="$C$">|; 

$key = q/{displaymath}{{bf{F}={{bf{I}'times{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="\begin{displaymath}
{\bf F} = {\bf I}' \times{\bf B},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}({{bf{r})=frac{1}{4pi,epsilon_0}intrho({{bf{r}'),frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="\begin{displaymath}
{\bf E}({\bf r}) =\frac{1}{4\pi  \epsilon_0}
\int \rho({\b...
...r}- {\bf r}' }
{\vert{\bf r} - {\bf r}'\vert^3}  d^3{\bf r}',
\end{displaymath}">|; 

$key = q/(nablatimes{{bf{B})_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$(\nabla\times{\bf B})_z$">|; 

$key = q/{displaymath}L_2=mu_0,N_2^{,2},pi,r^2,l.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1914.png"
 ALT="\begin{displaymath}
L_2 = \mu_0  N_2^{ 2}  \pi  r^2  l.
\end{displaymath}">|; 

$key = q/{displaymath}J^mu=rho_0,gamma(u),({{bf{u},c)=({{bf{j},rho,c),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2962.png"
 ALT="\begin{displaymath}
J^\mu = \rho_0 \gamma(u)  ({\bf u}, c) = ({\bf j}, \rho  c),
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2equivfrac{partial^2}{partialx^2}+frac{partial^2}{partialy^2}+frac{partial^2}{partialz^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="\begin{displaymath}
\nabla^2 \equiv \frac{\partial^2}{\partial x^2}+
\frac{\partial^2}{\partial y^2}+ \frac{\partial^2}{\partial z^2}
\end{displaymath}">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=left(frac{partialA_z}{partialy}-frac{partialA_y}{partialz}right),dS,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf l} = \left(\frac{\partial A_z}{\partial y}-
\frac{\partial A_y}{\partial z}\right) dS,
\end{displaymath}">|; 

$key = q/{displaymath}k^2,c^2=omega^2-omega_{mn}^{,2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2622.png"
 ALT="\begin{displaymath}
k^2 c^2 = \omega^2 - \omega_{mn}^{ 2},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{r}=r,(0,,sinalpha,,cosalpha),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3364.png"
 ALT="\begin{displaymath}
{\bf r} = r (0,  \sin\alpha,  \cos\alpha),
\end{displaymath}">|; 

$key = q/{displaymath}dtau^2=-frac{dx^2+dy^2+dz^2}{c^2}+dt^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2932.png"
 ALT="\begin{displaymath}
d\tau^2 = - \frac{dx^2+dy^2+dz^2}{c^2} + dt^2.
\end{displaymath}">|; 

$key = q/displaystylex,'sintheta+y',costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle x '\sin\theta +y' \cos\theta,$">|; 

$key = q/^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="$^2$">|; 

$key = q/{displaymath}phi(x,y)=C,exp(-n,x),sin(n,y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1626.png"
 ALT="\begin{displaymath}
\phi(x, y) = C  \exp(-n x) \sin (n y),
\end{displaymath}">|; 

$key = q/n_2>n_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2480.png"
 ALT="$n_2&gt; n_1$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1898.png"
 ALT="$t=0$">|; 

$key = q/(RslashR_0)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="$(R/R_0)^2$">|; 

$key = q/RsimR_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="$R\sim R_0$">|; 

$key = q/{{bf{B}_3={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1460.png"
 ALT="${\bf B}_3={\bf0}$">|; 

$key = q/costheta=c_astslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="$\cos\theta= c_\ast/v$">|; 

$key = q/rho=e,n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2957.png"
 ALT="$\rho = e n$">|; 

$key = q/{displaymath}{nabla}cdotleft(kappa,nablaTright)=c,frac{partialT}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="\begin{displaymath}
{\nabla}\cdot\left(\kappa  \nabla T\right) = c  \frac{\partial T}{\partial t}.
\end{displaymath}">|; 

$key = q/displaystyle-{T^4}_i=frac{epsilon^{ijk}E_jB_k}{mu_0,c},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3201.png"
 ALT="$\displaystyle - {T^4}_i = \frac{\epsilon^{ijk} E_j B_k}{\mu_0  c},$">|; 

$key = q/deltaz={{rm{i},deltay;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1554.png"
 ALT="$\delta z
= {\rm i} \delta y$">|; 

$key = q/A^{icdotsj}_{kcdotsl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2795.png"
 ALT="$A^{i\cdots j}_{k\cdots l}$">|; 

$key = q/displaystylez;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="$\displaystyle z$">|; 

$key = q/displaystylep_{mu}^{mu'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2889.png"
 ALT="$\displaystyle p_{\mu}^{\mu'}$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}=left(frac{partialA_x}{partialz}-frac{partialA_z}{partialx}right)dS_y.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="\begin{displaymath}
\oint {\bf A} \cdot d{\bf l} = \left(\frac{\partial A_x}{\partial z}-
\frac{\partial A_z}{\partial x}\right) dS_y.
\end{displaymath}">|; 

$key = q/%latex2htmlidmarker26264(ref{e9.147});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2467.png"
 ALT="% latex2html id marker 26264
$(\ref{e9.147})$">|; 

$key = q/dS=pi,r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="$dS = \pi  r^2$">|; 

$key = q/{displaymath}W=frac{1}{4pi,epsilon_0}int_{infty}^dfrac{q^2}{4,z^2},dz=frac{1}{4p{infty}^d=-frac{1}{4pi,epsilon_0}frac{q^2}{4,d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="430" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img1520.png"
 ALT="\begin{displaymath}
W = \frac{1}{4\pi  \epsilon_0}\int_{\infty}^d \frac{q^2}{4\...
...t]_{\infty}^d
= - \frac{1}{4\pi \epsilon_0} \frac{q^2}{4 d}.
\end{displaymath}">|; 

$key = q/{displaymath}nablaequivleft(frac{partial}{partialx},,frac{partial}{partialy},,frac{partial}{partialz}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="\begin{displaymath}
\nabla \equiv \left( \frac{\partial}{\partial x},  \frac{\partial}{\partial y}, 
\frac{\partial }{\partial z}\right),
\end{displaymath}">|; 

$key = q/{displaymath}frac{partialA_{kcdotsl}^{icdotsj}}{partialx^m}=A^{icdotsj}_{kcdotsl,m}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2823.png"
 ALT="\begin{displaymath}
\frac{\partial A_{k\cdots l}^{i\cdots j} }{\partial x^m} =
A^{i \cdots j}_{k\cdots l,m}.
\end{displaymath}">|; 

$key = q/{displaymath}delta({{bf{r}-{{bf{r}')=delta(x-x'),delta(y-y'),delta(z-z'),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="\begin{displaymath}
\delta({\bf r} - {\bf r}') = \delta(x-x') \delta(y-y') \delta(z-z'),
\end{displaymath}">|; 

$key = q/int_S{{bf{B}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="$\int_S {\bf B} \cdot d{\bf S}$">|; 

$key = q/|{{bf{u}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2111.png"
 ALT="$\vert{\bf u}\vert$">|; 

$key = q/{displaymath}{{bf{j}_m=nablatimes{{bf{M}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1773.png"
 ALT="\begin{displaymath}
{\bf j}_m = \nabla\times{\bf M}.
\end{displaymath}">|; 

$key = q/R^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2900.png"
 ALT="$R^\mu$">|; 

$key = q/{displaymath}{{bf{curl},{{bf{A}=left(frac{partialA_z}{partialy}-frac{partialA_y}lA_y}{partialx}-frac{partialA_x}{partialy}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="415" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="\begin{displaymath}
{\bf curl} {\bf A} = \left(\frac{\partial A_z}{\partial y}-...
...tial A_y}{\partial x}- \frac{\partial A_x}
{\partial y}\right)
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{2}left(epsilon_0,E^kE_k+frac{B^kB_k}{mu_0}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3203.png"
 ALT="$\displaystyle \frac{1}{2} \left(\epsilon_0  E^k E_k +\frac{B^k B_k}{\mu_0}\right).$">|; 

$key = q/displaystylefrac{{bf{j}{c,epsilon_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2973.png"
 ALT="$\displaystyle \frac{\bf j} {c \epsilon_0}.$">|; 

$key = q/x^{mu'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3289.png"
 ALT="$x^{\mu'}$">|; 

$key = q/displaystyle-a_xsintheta+a_ycostheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle -a_x\sin\theta + a_y\cos\theta,$">|; 

$key = q/-{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3014.png"
 ALT="$-{\bf B}$">|; 

$key = q/{displaymath}{{bf{g}=frac{{{bf{u}}{c^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img2146.png"
 ALT="\begin{displaymath}
{\bf g} = \frac{{\bf u}}{c^2}.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{[rho]}{R},dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int \frac{[\rho]}{R}  dV',$">|; 

$key = q/{displaymath}{{bf{r}_0={{bf{r}-frac{r}{c},{{bf{u}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3266.png"
 ALT="\begin{displaymath}
{\bf r}_0 = {\bf r} - \frac{r}{c} {\bf u}.
\end{displaymath}">|; 

$key = q/pmQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$\pm Q$">|; 

$key = q/displaystyleoint_{S}{{bf{E}_2cdotd{{bf{S}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1435.png"
 ALT="$\displaystyle \oint_{S} {\bf E}_2\cdot d{\bf S}_i$">|; 

$key = q/displaystyleleftlgrouparray{{cccc}+gamma<col_mark>0<col_mark>0<col_mark>+gamma,b,beta<col_mark>0<col_mark>0<col_mark>+gammaarray{rightrgroup.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="111" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2892.png"
 ALT="$\displaystyle \left\lgroup
\begin{array}{cccc}
+\gamma &amp; 0 &amp; 0 &amp; +\gamma \beta...
...\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
+\gamma \beta &amp; 0 &amp; 0 &amp; +\gamma
\end{array}\right\rgroup.$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2078.png"
 ALT="$K$">|; 

$key = q/{displaymath}W_3=frac{1}{4pi,epsilon_0}left(frac{q_3,q_1}{|{{bf{r}_3-{{bf{r}_1|}+frac{q_3,q_2}{|{{bf{r}_3-{{bf{r}_2|}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="\begin{displaymath}
W_3 = \frac{1}{4\pi  \epsilon_0} \left( \frac{q_3  q_1}{\v...
...t}
+ \frac{q_3  q_2}{\vert{\bf r}_3 - {\bf r}_2\vert}\right).
\end{displaymath}">|; 

$key = q/omega=k,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2343.png"
 ALT="$\omega = k c$">|; 

$key = q/(A_1,A_2,cdots,A_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2770.png"
 ALT="$(A_1, A_2, \cdots, A_n)$">|; 

$key = q/{displaymath}p=frac{langleUrangle}{3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2161.png"
 ALT="\begin{displaymath}
p = \frac{ \langle U\rangle}{3}.
\end{displaymath}">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1685.png"
 ALT="$\epsilon$">|; 

$key = q/{displaymath}I_z=frac{langle{{bf{E}times{{bf{B}cdothat{{bf{z}rangle}{mu_0}=frac{heta}{2,mu_0}=frac{E_0^{,2},costheta}{2,mu_0,v}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2543.png"
 ALT="\begin{displaymath}
I_z =\frac{\langle {\bf E}\times{\bf B}\cdot\hat{\bf z}\rang...
...\theta}{2 \mu_0} = \frac{E_0^{ 2} \cos\theta}{2 \mu_0 v}.
\end{displaymath}">|; 

$key = q/{displaymath}P_{{rm{load}=langleI^2R_{{rm{load}rangle=frac{R_{{rm{load},V_0^{,2}}{2,(R_{{rm{rad}+R_{{rm{load})^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2248.png"
 ALT="\begin{displaymath}
P_{\rm load} = \langle I^2 R_{\rm load}\rangle = \frac{R_{\rm load}  V_0^{ 2}}
{2 (R_{\rm rad} + R_{\rm load})^2}.
\end{displaymath}">|; 

$key = q/partialE_yslashpartialy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$\partial E_y/\partial y$">|; 

$key = q/displaystyleint_0^ar^3,drint_0^{pislash2}sintheta,costheta,dthetaint_0^{2pi}dphi=frac{pi,a^4}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$\displaystyle \int_0^a r^3 dr \int_0^{\pi/2} \sin\theta  \cos\theta d\theta \int_0^{2\pi}
d\phi = \frac{\pi  a^4}{4},$">|; 

$key = q/r^m,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1734.png"
 ALT="$r^m \cos\theta$">|; 

$key = q/{mitDelta}varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2391.png"
 ALT="${\mit\Delta}\varphi$">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\gamma$">|; 

$key = q/{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1882.png"
 ALT="${\mit\Phi}$">|; 

$key = q/x'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2706.png"
 ALT="$x'=0$">|; 

$key = q/{displaymath}int_{P}^Qf(x,y),dl={{rm{Area~under~the~curve}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="\begin{displaymath}
\int_{P}^Q f(x,y) dl = {\rm Area&nbsp;under&nbsp;the&nbsp;curve}.
\end{displaymath}">|; 

$key = q/A^mu=(c,{{bf{A},phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3108.png"
 ALT="$A^\mu= (c {\bf A}, \phi)$">|; 

$key = q/nneqm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1644.png"
 ALT="$n\neq m$">|; 

$key = q/{displaymath}left[int_{x_1}^{x_2}D(x,y),dxright],dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="\begin{displaymath}
\left[\int_{x_1}^{x_2} D(x,y) dx\right] dy.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E}_i,{{rm{e}^{,{{rm{i},({{bf{k}_icdot{{bf{r}-omega,t)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2494.png"
 ALT="$\displaystyle {\bf E}_i {\rm e}^{ {\rm i} ({\bf k}_i\cdot{\bf r}-\omega t)},$">|; 

$key = q/I_1(t=0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1930.png"
 ALT="$I_1(t=0)=0$">|; 

$key = q/{{bf{j}_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1772.png"
 ALT="${\bf j}_m$">|; 

$key = q/{displaymath}{{bf{f}=e,({{bf{E}+{{bf{u}times{{bf{B}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3170.png"
 ALT="\begin{displaymath}
{\bf f} = e ({\bf E} + {\bf u}\times {\bf B}).
\end{displaymath}">|; 

$key = q/{displaymath}nablacdotleft(frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3}right)=-nr}-{{bf{r}'|}right)=4pi,delta({{bf{r}-{{bf{r}'),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="\begin{displaymath}
\nabla\cdot\left(\frac{{\bf r} - {\bf r}'}{\vert{\bf r} - {\...
...f r} - {\bf r}'\vert}\right)= 4\pi \delta({\bf r}
-{\bf r}'),
\end{displaymath}">|; 

$key = q/displaystyleu_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2731.png"
 ALT="$\displaystyle u_2$">|; 

$key = q/d{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2282.png"
 ALT="$d{\mit\Omega}$">|; 

$key = q/displaystylev_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="$\displaystyle v_\parallel,$">|; 

$key = q/k_+=k_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2382.png"
 ALT="$k_+=k_-$">|; 

$key = q/{displaymath}R_{{rm{rad}=789left(frac{l}{lambda}right)^2,{{rm{ohms}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2237.png"
 ALT="\begin{displaymath}
R_{\rm rad} = 789 \left(\frac{l}{\lambda}\right)^2 {\rm ohms}.
\end{displaymath}">|; 

$key = q/{displaymath}W=int_{infty}^0frac{-y,dy}{(a^2+y^2)^{3slash2}}=left[frac{1}{(y^2+a^2)^{1slash2}}right]_0^infty=frac{1}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="\begin{displaymath}
W = \int_{\infty}^0 \frac{-y dy}{(a^2 + y^2)^{3/2}} = \left[\frac{1}{(y^2+a^2)^{1/2}}
\right]_0^\infty = \frac{1}{a}.
\end{displaymath}">|; 

$key = q/{displaymath}left.frac{partialphi}{partialr}right|_{r=a+}=left.epsilon,frac{partialphi}{partialr}right|_{r=a-}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1733.png"
 ALT="\begin{displaymath}
\left.\frac{\partial \phi}{\partial r}\right\vert _{r=a+} = ...
...\epsilon 
\frac{\partial\phi}{\partial r}\right\vert _{r=a-}.
\end{displaymath}">|; 

$key = q/{displaymath}U^mu=frac{dx^mu}{dtau}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2943.png"
 ALT="\begin{displaymath}
U^\mu = \frac{dx^\mu}{d\tau}
\end{displaymath}">|; 

$key = q/S_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$S_x$">|; 

$key = q/dV'=d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="$dV' = d^3 {\bf r}'$">|; 

$key = q/{displaymath}M=mu_0,N_1,N_2,pi,r^2,l.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1912.png"
 ALT="\begin{displaymath}
M = \mu_0  N_1  N_2  \pi  r^2  l.
\end{displaymath}">|; 

$key = q/{displaymath}frac{dsigma}{d{mitOmega}}=frac{dPslashd{mitOmega}}{|langle{{bf{u}rangle|},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2280.png"
 ALT="\begin{displaymath}
\frac{d\sigma}{d{\mit\Omega}} = \frac{dP/d{\mit\Omega}}{\vert\langle{\bf u}\rangle\vert},
\end{displaymath}">|; 

$key = q/dV=dl_i,A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1993.png"
 ALT="$dV = dl_i  A_i$">|; 

$key = q/{displaymath}E_{parallel,A}-E_{parallel,B}=0:{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="\begin{displaymath}
E_{\parallel A} - E_{\parallel B}=0:
\end{displaymath}">|; 

$key = q/E^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3337.png"
 ALT="$E^4$">|; 

$key = q/10^{18},{{rm{Hz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2414.png"
 ALT="$10^{18} {\rm Hz}$">|; 

$key = q/displaystylefrac{Q_{{rm{total}}{epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1436.png"
 ALT="$\displaystyle \frac{Q_{\rm total}} {\epsilon_0}$">|; 

$key = q/n({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$n({\bf r})$">|; 

$key = q/{displaymath}frac{4pi}{mu_0,e},{{bf{B}=nablatimesfrac{{bf{u}{s}=-frac{nabla'stimac{{{bf{u}}{s^2}frac{partials}{partialt'}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3257.png"
 ALT="\begin{displaymath}
\frac{4\pi}{\mu_0 e}  {\bf B} = \nabla\times\frac{\bf u}{s...
... - \frac{{\bf u}}{s^2} \frac{\partial s}{\partial t'}
\right),
\end{displaymath}">|; 

$key = q/displaystyle-left(frac{epsilon_2-epsilon_1}{epsilon_2+epsilon_1}right)q,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1719.png"
 ALT="$\displaystyle -\left(\frac{\epsilon_2-\epsilon_1}{\epsilon_2 + \epsilon_1}
\right) q,$">|; 

$key = q/{figure}{epsfysize{=1.5in{centerline{epsffile{fig7.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="170" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="\begin{figure}
\epsfysize =1.5in
\centerline{\epsffile{fig7.eps}}
\end{figure}">|; 

$key = q/displaystyle{{bf{0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="$\displaystyle {\bf0}.$">|; 

$key = q/{displaymath}P_{{rm{rad}=frac{omega^2,l^2,I_0^{,2}}{32pi^2,epsilon_0,c^3}int_0^{_0^pifrac{sin^2theta}{r^2},,r^2sintheta,,dtheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2231.png"
 ALT="\begin{displaymath}
P_{\rm rad} = \frac{\omega^2  l^2  I_0^{ 2}}{32\pi^2  \e...
...0^\pi \frac{\sin^2\theta}{r^2}    r^2\sin\theta  
d\theta.
\end{displaymath}">|; 

$key = q/displaystyle-frac{partial{{bf{A}}{partialt}-nablaphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2223.png"
 ALT="$\displaystyle - \frac{\partial {\bf A}}{\partial t} - \nabla \phi,$">|; 

$key = q/{displaymath}V(Q+dx)=V(Q)+int_Q^{Q+dx}{{bf{A}cdotd{{bf{l}=V(Q)+A_x,dx.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="\begin{displaymath}
V(Q+dx) = V(Q) + \int_Q^{Q+dx} {\bf A}\cdot d{\bf l} = V(Q) + A_x dx.
\end{displaymath}">|; 

$key = q/{r'}^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3139.png"
 ALT="${r'}^3$">|; 

$key = q/r=|{{bf{r}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="$r= \vert{\bf r}\vert$">|; 

$key = q/displaystyleE_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2360.png"
 ALT="$\displaystyle E_\pm$">|; 

$key = q/A_{{rm{eff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2257.png"
 ALT="$A_{\rm eff}$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}=frac{e^2,dot{u}^2}{16pi^2,epsilon_0,c^3}fuslashc)-costheta]^2}{[1-(uslashc),costheta]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3373.png"
 ALT="\begin{displaymath}
\frac{d P(t')}{d{\mit\Omega}} = \frac{e^2  \dot{u}^2}{16\pi...
... c^3}
\frac{[(u/c) - \cos\theta]^2}{[1-(u/c) \cos\theta]^5}.
\end{displaymath}">|; 

$key = q/{displaymath}u({{bf{r})=-frac{1}{4pi}intfrac{v({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="\begin{displaymath}
u({\bf r}) = -\frac{1}{4\pi} \int \frac{v({\bf r}')}{\vert{\bf r} - {\bf r}'\vert} d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{4piepsilon_0}intleft(frac{[rho]}{R^3},{{bf{R}+frac{[partialrhoslashpartialt]}{cR^2},{{bf{R}right),dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$\displaystyle - \frac{1}{4\pi\epsilon_0} \int \left(
\frac{[\rho]}{R^3} {\bf R} + \frac{[\partial\rho/\partial t]}{cR^2} {\bf R} \right)  dV',$">|; 

$key = q/100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="$100$">|; 

$key = q/{displaymath}P_{{rm{load}=P_{{rm{rad}=frac{V_0^{,2}}{8,R_{{rm{rad}}=frac{P_{{rm{in}}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2253.png"
 ALT="\begin{displaymath}
P_{\rm load} = P_{\rm rad} = \frac{V_0^{ 2}}{8  R_{\rm rad}} = \frac{P_{\rm in}}{2}.
\end{displaymath}">|; 

$key = q/B_3^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1469.png"
 ALT="$B_3^{ 2}$">|; 

$key = q/{displaymath}E_0-E_0,alpha=E_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1738.png"
 ALT="\begin{displaymath}
E_0 - E_0 \alpha = E_1.
\end{displaymath}">|; 

$key = q/{displaymath}m_e,frac{d^2z}{dt^2}=-e,E_0,sin(omega,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2273.png"
 ALT="\begin{displaymath}
m_e \frac{d^2 z}{dt^2} = -e E_0 \sin(\omega t),
\end{displaymath}">|; 

$key = q/E_perp,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="$E_\perp  A$">|; 

$key = q/{displaymath}Y,frac{d^2Y}{dx^2}+X,frac{d^2Y}{dy^2}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1607.png"
 ALT="\begin{displaymath}
Y  \frac{d^2 Y}{d x^2} + X \frac{d^2 Y}{d y^2} = 0.
\end{displaymath}">|; 

$key = q/displaystylefrac{x'+v,t'}{(1-v^2slashc^2)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2722.png"
 ALT="$\displaystyle \frac{x'+v t'}{(1-v^2/c^2)^{1/2}},$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=frac{1}{epsilon_0}int_Vrho({{bf{r}),d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="\begin{displaymath}
\oint_S {\bf E}\cdot d{\bf S} = \frac{1}{\epsilon_0} \int_V \rho({\bf r}) d^3{\bf r}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{j}=frac{partial{{bf{P}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2310.png"
 ALT="\begin{displaymath}
{\bf j} = \frac{\partial{\bf P}}{\partial t}.
\end{displaymath}">|; 

$key = q/u_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$u_2$">|; 

$key = q/{{bf{a}(t+deltat);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="${\bf a}(t+\delta t)$">|; 

$key = q/{displaymath}t-|{{bf{r}-z',hat{{bf{z}|slashcsimeqt-rslashc.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2213.png"
 ALT="\begin{displaymath}
t - \vert{\bf r} - z'  \hat{\bf z}\vert/c \simeq t - r/c.
\end{displaymath}">|; 

$key = q/{displaymath}nabla_{x'}=costheta,nabla_x+sintheta,nabla_y.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="\begin{displaymath}
\nabla_{x'} = \cos\theta  \nabla_x + \sin\theta  \nabla_y.
\end{displaymath}">|; 

$key = q/oint{{bf{v}cdotd{{bf{l}=2pi,r,omega,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$\oint {\bf v}\cdot d{\bf l} = 2\pi  r  \omega  r$">|; 

$key = q/{displaymath}I=-rho(x),v(x),A,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1481.png"
 ALT="\begin{displaymath}
I = -\rho(x) v(x) A,
\end{displaymath}">|; 

$key = q/A=pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2703.png"
 ALT="$A=\pm 1$">|; 

$key = q/{{bf{b}equiv(b_x,b_y,b_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="${\bf b} \equiv (b_x, b_y, b_z)$">|; 

$key = q/{displaymath}U=W_i=0?{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="\begin{displaymath}
U=W_i =0 ?
\end{displaymath}">|; 

$key = q/{displaymath}V_0,exp({{rm{i},omega,t)=I_0,exp({{rm{i},omega,t)R+L,{{rm{i},omega,+frac{I_0exp({{rm{i},omega,t)}{{{rm{i},omega,C},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2011.png"
 ALT="\begin{displaymath}
V_0  \exp({\rm i} \omega  t) =I_0   \exp({\rm i} \omega...
...t)
+\frac{I_0 \exp({\rm i} \omega  t)}{{\rm i} \omega  C},
\end{displaymath}">|; 

$key = q/displaystyleg_{munu},dx^{mu},dx^{nu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2866.png"
 ALT="$\displaystyle g_{\mu \nu}  dx^{\mu}  dx^{\nu},$">|; 

$key = q/displaystylefrac{b}{a+b}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1380.png"
 ALT="$\displaystyle \frac{b}{a+b}.$">|; 

$key = q/{displaymath}nablacdot({{bf{E}times{{bf{B})equiv{{bf{B}cdotnablatimes{{bf{E}-{{bf{E}cdotnablatimes{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2119.png"
 ALT="\begin{displaymath}
\nabla\cdot({\bf E}\times{\bf B}) \equiv {\bf B}\cdot\nabla\times{\bf E} - {\bf E}
\cdot \nabla\times{\bf B},
\end{displaymath}">|; 

$key = q/I_0^{,2}Rslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2239.png"
 ALT="$ I_0^{ 2}R/2$">|; 

$key = q/{{bf{r}_usimeq{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3272.png"
 ALT="${\bf r}_u \simeq{\bf r}$">|; 

$key = q/t';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="$t'$">|; 

$key = q/{displaymath}p=,langleUranglesimeq4times10^{-6},{{rm{N,m^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2165.png"
 ALT="\begin{displaymath}
p =  \langle U\rangle \simeq 4\times 10^{-6} {\rm N  m^{-2}}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitDelta}t=frac{{mitDelta}theta}{omega_0}left(1-frac{u}{c}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img3397.png"
 ALT="\begin{displaymath}
{\mit\Delta} t = \frac{{\mit\Delta} \theta}{\omega_0} \left(1-\frac{u}{c}\right),
\end{displaymath}">|; 

$key = q/{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="${\bf B}$">|; 

$key = q/s=r-{{bf{r}!cdot!{{bf{u}slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3238.png"
 ALT="$s = r - {\bf r}\!\cdot\!{\bf u}/c$">|; 

$key = q/{displaymath}r'=r,gamma,left(-frac{c,t}{r}+frac{v,x}{c,r}right)=r,gammaleft(1+frac{v}{c}costhetaright),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2991.png"
 ALT="\begin{displaymath}
r' = r \gamma \left(-\frac{c t}{r} + \frac{v x}{c r}\right)
= r \gamma \left(1 + \frac{v}{c} \cos\theta\right),
\end{displaymath}">|; 

$key = q/displaystylemu_0,{{bf{j}+epsilon_0mu_0frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="$\displaystyle \mu_0  {\bf j}+ \epsilon_0\mu_0
\frac{\partial {\bf E}}{\partial
t}.$">|; 

$key = q/{displaymath}{{bf{B}_1({{bf{r})=frac{mu_0,I_1}{4pi}oint_{{rm{loop,1}frac{d{{bf{l1times({{bf{r}-{{bf{r}')}{|{{bf{r}-{{bf{r}'|^3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1865.png"
 ALT="\begin{displaymath}
{\bf B}_1({\bf r}) = \frac{\mu_0  I_1}{4\pi} \oint_{\rm loo...
... \times ({\bf r} - {\bf r}')}{\vert{\bf r} - {\bf r}'\vert^3},
\end{displaymath}">|; 

$key = q/-1.6times10^{-19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$-1.6\times 10^{-19}$">|; 

$key = q/phi=phi(x^1,cdots,x^n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2802.png"
 ALT="$\phi=\phi(x^1, \cdots, x^n)$">|; 

$key = q/displaystyle-frac{partialB_z}{partialy}+{{rm{i},k,B_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2584.png"
 ALT="$\displaystyle - \frac{\partial B_z}{\partial y} + {\rm i} k B_y,$">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{l}=-frac{partial}{partialt}int_S{{bf{B}cdotd{{bf{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="\begin{displaymath}
\oint_C {\bf E} \cdot d{\bf l} = -\frac{\partial}{\partial t} \int_S {\bf B}\cdot
d{\bf S}
\end{displaymath}">|; 

$key = q/(x',y',z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$(x', y', z')$">|; 

$key = q/displaystylenablatimes{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="$\displaystyle \nabla\times{\bf A}$">|; 

$key = q/M_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1868.png"
 ALT="$M_{21}$">|; 

$key = q/theta_{{rm{max}rightarrow1slash(2,gamma);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3350.png"
 ALT="$\theta_{\rm max} \rightarrow 1/(2 \gamma)$">|; 

$key = q/R=|{{bf{r}-{{bf{r}'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="$R = \vert{\bf r} - {\bf r}'\vert$">|; 

$key = q/{displaymath}{{bf{E}({{bf{r})=frac{1}{4piepsilon_0}intrho({{bf{r}'),frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="\begin{displaymath}
{\bf E} ({\bf r}) = \frac{1}{4\pi\epsilon_0} \int\rho({\bf r...
...f r} - {\bf r}'}{\vert{\bf r} - {\bf r}'\vert^3} d^3{\bf r}',
\end{displaymath}">|; 

$key = q/{displaymath}frac{V_2(t=0)}{V_1}=k,frac{N_2}{N_1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1939.png"
 ALT="\begin{displaymath}
\frac{V_2(t=0)}{V_1} = k  \frac{N_2}{N_1},
\end{displaymath}">|; 

$key = q/displaystylefrac{t'+v,x'slashc^2}{(1-v^2slashc^2)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2726.png"
 ALT="$\displaystyle \frac{t'+v x'/c^2}{(1-v^2/c^2)^{1/2}}.$">|; 

$key = q/{displaymath}V=oint{{bf{E}cdotd{{bf{l}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="\begin{displaymath}
V = \oint {\bf E} \cdot d{\bf l} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}u({{bf{r})rightarrow0mbox{hspace{1cm}as{|{{bf{r}|rightarrowinfty{and{|t|rightarrowinfty{.}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="\begin{displaymath}
u({\bf r})\rightarrow 0 \mbox{\hspace{1cm} as $\vert{\bf r}\vert\rightarrow\infty$ and $\vert t\vert\rightarrow
\infty$.}
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{B^2}{2,mu_0},V,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1973.png"
 ALT="\begin{displaymath}
W = \frac{B^2}{2 \mu_0} V,
\end{displaymath}">|; 

$key = q/chi_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1682.png"
 ALT="$\chi_e$">|; 

$key = q/g_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2830.png"
 ALT="$g_{ij}$">|; 

$key = q/oint{{bf{v}cdotd{{bf{l}slashdS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$\oint {\bf v}\cdot d{\bf l}/ dS$">|; 

$key = q/{displaymath}int_P^Qleft(f,dx+g,dyright)=F(Q)-F(P){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="\begin{displaymath}
\int_P^Q \left(f dx + g dy\right) = F(Q) - F(P)
\end{displaymath}">|; 

$key = q/psi({{bf{r},t)rightarrowpsi({{bf{r})+c,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="$\psi({\bf r}, t)\rightarrow \psi({\bf r}) + c t$">|; 

$key = q/|G|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$\vert G\vert\rightarrow \infty$">|; 

$key = q/displaystyleepsilon_2,E_z(z=0^-),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1699.png"
 ALT="$\displaystyle \epsilon_2  E_z (z=0^-),$">|; 

$key = q/j_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="$j_z$">|; 

$key = q/displaystylenabla^2A_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="$\displaystyle \nabla^2 A_y$">|; 

$key = q/dt'=gamma,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3314.png"
 ALT="$dt'=\gamma  dt$">|; 

$key = q/{displaymath}nablaR=frac{{bf{R}{R},~~~nabla(R^{-1})=-frac{{bf{R}{R^3},~~~nablat_r=-frac{{bf{R}{cR}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="\begin{displaymath}
\nabla R = \frac{\bf R}{R},&nbsp;&nbsp;&nbsp;\nabla( R^{-1})= - \frac{\bf R}{R^3},&nbsp;&nbsp;&nbsp;\nabla t_r = - \frac{\bf R}{cR}.
\end{displaymath}">|; 

$key = q/B,pi,r^2=mu_0,N,I,pi,r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1886.png"
 ALT="$B \pi  r^2=
\mu_0  N  I \pi  r^2$">|; 

$key = q/{displaymath}epsilon_0mu_0frac{partial^2{{bf{A}}{partialt^2}-nabla^2{{bf{A}=mu_0+epsilon_0mu_0,frac{partialphi}{partialt}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="\begin{displaymath}
\epsilon_0 \mu_0 \frac{\partial^2 {\bf A}}{\partial t^2} - \...
...A} +\epsilon_0\mu_0  \frac{\partial\phi}
{\partial t}\right).
\end{displaymath}">|; 

$key = q/R+T=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2489.png"
 ALT="$R+T=1$">|; 

$key = q/{displaymath}nablacdotnablaphi=nabla^2phi=left(frac{partial^2phi}{partialx^2}+frpartialy^2}+frac{partial^2phi}{partialz^2}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="\begin{displaymath}
\nabla\cdot\nabla \phi = \nabla^2 \phi = \left(\frac{\partia...
...phi}{\partial y^2}+\frac{\partial^2 \phi}{\partial z^2}\right)
\end{displaymath}">|; 

$key = q/nablatimesnablaphi={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="$\nabla\times\nabla \phi = {\bf0}$">|; 

$key = q/s_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2373.png"
 ALT="$s_+$">|; 

$key = q/{displaymath}{{bf{B}({{bf{r})=frac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r}')times({{bfr}-{{bf{r}')}{|{{bf{r}-{{bf{r}'|^3},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="\begin{displaymath}
{\bf B} ({\bf r}) = \frac{\mu_0}{4\pi} \int \frac{{\bf j}({\...
...r} - {\bf r}')}
{\vert{\bf r} - {\bf r}'\vert^3} d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{mitDelta}omega,{mitDelta}tsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3400.png"
 ALT="${\mit\Delta}\omega {\mit\Delta} t\sim 1$">|; 

$key = q/{displaymath}nabla^2T=frac{partial^2T}{partialx^2}+frac{partial^2T}{partialy^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="\begin{displaymath}
\nabla^2 T = \frac{\partial^2 T}{\partial x^2}+ \frac{\partial ^2 T}{\partial y^2}.
\end{displaymath}">|; 

$key = q/{displaymath}varphi=tan^{-1}(E_yslashE_x)={mitDelta}k,z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2386.png"
 ALT="\begin{displaymath}
\varphi = \tan^{-1}(E_y/E_x) = {\mit\Delta}k z.
\end{displaymath}">|; 

$key = q/(x,y,z,c,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2988.png"
 ALT="$(x,y,z,c t)$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\alpha$">|; 

$key = q/{displaymath}frac{omega}{k},frac{domega}{dk}=v_p,v_g=c^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2344.png"
 ALT="\begin{displaymath}
\frac{\omega}{k} \frac{d\omega}{dk} = v_p v_g= c^2.
\end{displaymath}">|; 

$key = q/{displaymath}partial_iE^i=partial_iF^{i4}+partial_4F^{44}=frac{J^4}{c,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3049.png"
 ALT="\begin{displaymath}
\partial_i E^i = \partial_i F^{i4} +\partial_4 F^{44} = \frac{J^4}{c \epsilon_0}.
\end{displaymath}">|; 

$key = q/displaystylefrac{E_i}{v_1},left(-costheta_i,,0,,sintheta_iright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2525.png"
 ALT="$\displaystyle \frac{E_i}{v_1} \left(-\cos\theta_i, 0, \sin\theta_i\right),$">|; 

$key = q/displaystylefrac{Q_i}{epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1432.png"
 ALT="$\displaystyle \frac{Q_i} {\epsilon_0}$">|; 

$key = q/z>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1485.png"
 ALT="$z&gt;0$">|; 

$key = q/phi=V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1419.png"
 ALT="$\phi=V$">|; 

$key = q/N,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1887.png"
 ALT="$N l$">|; 

$key = q/{displaymath}epsilon^{ijk}partial_jE_k=epsilon^{ijk}partial_j(1slash2,epsilon_{kab}E^{ab})=partial_jE^{ij}=-partial_4,(c,B^i),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3086.png"
 ALT="\begin{displaymath}
\epsilon^{ijk}\partial_j E_k = \epsilon^{ijk}\partial_j
(1/2...
...on_{kab} E^{ab}) = \partial_j E^{ij} = -\partial_4  (c B^i),
\end{displaymath}">|; 

$key = q/g_{11}=g_{22}=g_{33}=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2869.png"
 ALT="$g_{11}=g_{22}=g_{33}=-1$">|; 

$key = q/{{bf{a}=d{{bf{u}slash{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2947.png"
 ALT="${\bf a} = d{\bf u}/{dt}$">|; 

$key = q/(l,m,n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2694.png"
 ALT="$(l, m, n)$">|; 

$key = q/{displaymath}U=frac{1}{2},{{bf{E}cdot{{bf{D}+frac{1}{2},{{bf{B}cdot{{bf{H},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2133.png"
 ALT="\begin{displaymath}
U = \frac{1}{2} {\bf E}\cdot{\bf D} + \frac{1}{2} {\bf B}\cdot{\bf H},
\end{displaymath}">|; 

$key = q/u_1+u_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="$u_1+u_2$">|; 

$key = q/displaystylenablacdot{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$\displaystyle \nabla\cdot{\bf E}$">|; 

$key = q/{{bf{a}cdot{{bf{a}times{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="${\bf a}\cdot {\bf a}\times{\bf b}$">|; 

$key = q/{displaymath}W_{{rm{analogue}=-frac{1}{4pi,epsilon_0}frac{q^2}{2,d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1507.png"
 ALT="\begin{displaymath}
W_{\rm analogue} = - \frac{1}{4\pi \epsilon_0} \frac{q^2}{2 d}.
\end{displaymath}">|; 

$key = q/-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1583.png"
 ALT="$-x$">|; 

$key = q/{displaymath}E_i+E_r=E_t.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2468.png"
 ALT="\begin{displaymath}
E_i + E_r = E_t.
\end{displaymath}">|; 

$key = q/{displaymath}M,x=m,L=frac{E}{c^2},L.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2138.png"
 ALT="\begin{displaymath}
M  x = m  L = \frac{E}{c^2}  L.
\end{displaymath}">|; 

$key = q/^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2163.png"
 ALT="$^{-2}$">|; 

$key = q/{displaymath}B_0+2,B_0,alpha=,B_1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1825.png"
 ALT="\begin{displaymath}
B_0 + 2 B_0 \alpha =  B_1.
\end{displaymath}">|; 

$key = q/kcdotsl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2797.png"
 ALT="$k\cdots l$">|; 

$key = q/{displaymath}nablaUcdotnablaV=frac{partialU}{partialx}frac{partialV}{partialx}+frac{partialU}{partialy}frac{partialV}{partialy}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1569.png"
 ALT="\begin{displaymath}
\nabla U \cdot \nabla V = \frac{\partial U}{\partial x}\frac...
...
+\frac{\partial U}{\partial y} \frac{\partial V}{\partial y}.
\end{displaymath}">|; 

$key = q/{displaymath}intB_3^{,2},dV=int{{bf{A}_3times{{bf{B}_3cdot{{bf{dS}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1465.png"
 ALT="\begin{displaymath}
\int B_3^{ 2} dV = \int {\bf A}_3\times{\bf B}_3\cdot{\bf dS}.
\end{displaymath}">|; 

$key = q/displaystyleR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2485.png"
 ALT="$\displaystyle R$">|; 

$key = q/eta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="$\eta = 0$">|; 

$key = q/{displaymath}left.mu_0,frac{partialphi_m}{partialr}right|_{r=a+}=left.mu,frac{partialphi_m}{partialr}right|_{r=a-}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1821.png"
 ALT="\begin{displaymath}
\left.\mu_0 \frac{\partial \phi_m}{\partial r}\right\vert _...
...ft.\mu 
\frac{\partial\phi_m}{\partial r}\right\vert _{r=a-}.
\end{displaymath}">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\beta$">|; 

$key = q/dT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$dT$">|; 

$key = q/{displaymath}{{bf{u}=frac{{{bf{E}times{{bf{B}}{mu_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2125.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{{\bf E}\times{\bf B}}{\mu_0}
\end{displaymath}">|; 

$key = q/{displaymath}P=q,{{bf{v}cdot{{bf{E}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="\begin{displaymath}
P = q {\bf v}\cdot {\bf E}.
\end{displaymath}">|; 

$key = q/10^5,mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1802.png"
 ALT="$10^5 \mu_0$">|; 

$key = q/phi(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1476.png"
 ALT="$\phi(x)$">|; 

$key = q/displaystyleB_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3280.png"
 ALT="$\displaystyle B_\phi$">|; 

$key = q/displaystylem_e,omega^2,x=e,(E_x-{{rm{i},omega,B_0,y),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2356.png"
 ALT="$\displaystyle m_e \omega^2 x = e (E_x - {\rm i} \omega B_0 y),$">|; 

$key = q/displaystylefrac{E_t}{v_2},hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2551.png"
 ALT="$\displaystyle \frac{E_t}{v_2} \hat{\bf y},$">|; 

$key = q/{{rm{TE}_{mn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2619.png"
 ALT="${\rm TE}_{mn}$">|; 

$key = q/dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$dz$">|; 

$key = q/phi=phi(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2644.png"
 ALT="$\phi=\phi(r)$">|; 

$key = q/{{bf{r}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="${\bf r}_3$">|; 

$key = q/displaystyle{{bf{E}(z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2449.png"
 ALT="$\displaystyle {\bf E}(z,t)$">|; 

$key = q/{displaymath}frac{1}{c^2}frac{partialphi}{partialt}+nabla!cdot!{{bf{A}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2977.png"
 ALT="\begin{displaymath}
\frac{1}{c^2} \frac{\partial\phi}{\partial t} + \nabla\!\cdot\! {\bf A} =0.
\end{displaymath}">|; 

$key = q/{{bf{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="${\bf f}$">|; 

$key = q/pmq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="$\pm q$">|; 

$key = q/{displaymath}I(x,t)=frac{V_0}{Z_0}exp[{{rm{i},(omega,t-k,x)]-frac{K,V_0}{Z_0}exp[{{rm{i},(omega,t+k,x)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="438" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2079.png"
 ALT="\begin{displaymath}
I(x, t) = \frac{V_0}{Z_0} \exp[{\rm i} (\omega  t - k x)] - \frac{K  V_0}{Z_0}
\exp[{\rm i} (\omega  t + k x)].
\end{displaymath}">|; 

$key = q/{displaymath}f=frac{d(m,u)}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img3157.png"
 ALT="\begin{displaymath}
f = \frac{d(m u)}{dt},
\end{displaymath}">|; 

$key = q/dx'^2+dy'^2+dz'^2-c^2,dt'^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2689.png"
 ALT="$dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2$">|; 

$key = q/nablatimes{{bf{B}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="$\nabla\times{\bf B} = {\bf0}$">|; 

$key = q/epsilon_1,E_{z,1}=epsilon_2,E_{z,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2556.png"
 ALT="$\epsilon_1 E_{z 1} = \epsilon_2 E_{z 2}$">|; 

$key = q/{displaymath}F^{mu'nu'}=F^{munu},p_mu^{mu'},p_{nu}^{nu'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img3092.png"
 ALT="\begin{displaymath}
F^{\mu'\nu'} = F^{\mu\nu}  p_\mu^{\mu'}  p_{\nu}^{\nu'}.
\end{displaymath}">|; 

$key = q/displaystyleT^{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3208.png"
 ALT="$\displaystyle T^{i4}$">|; 

$key = q/{displaymath}V=I,R,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="\begin{displaymath}
V = I  R,
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{l}=int_Snablatimes{{bf{B}cdotd{{bf{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="\begin{displaymath}
\oint_C {\bf B} \cdot d{\bf l} = \int_S \nabla\times{\bf B} \cdot d{\bf S},
\end{displaymath}">|; 

$key = q/pislash2<theta<pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3375.png"
 ALT="$\pi/2&lt;\theta&lt;\pi$">|; 

$key = q/LslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1905.png"
 ALT="$L/R$">|; 

$key = q/x=-l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2076.png"
 ALT="$x=-l$">|; 

$key = q/{displaymath}V_2=V_1,k,frac{N_2}{N_1},exp(-R_1,tslashL_1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1936.png"
 ALT="\begin{displaymath}
V_2 = V_1  k  \frac{N_2}{N_1}  \exp(-R_1  t/L_1).
\end{displaymath}">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0,r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3106.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0 r'},$">|; 

$key = q/displaystylea_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3151.png"
 ALT="$\displaystyle a_0$">|; 

$key = q/displaystyle-frac{1}{4pi,epsilon_0}intfrac{[partial{{bf{j}_perpslashpartialt]}{c^2,R},dV',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="$\displaystyle -\frac{1}{4\pi \epsilon_0}\int\frac{[\partial {\bf j}_\perp /\partial t]}{c^2  R}
 dV',$">|; 

$key = q/{displaymath}phi_3=phi_1-phi_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1407.png"
 ALT="\begin{displaymath}
\phi_3 = \phi_1 - \phi_2.
\end{displaymath}">|; 

$key = q/{{bf{r}_u={{bf{r}-r,{{bf{u}slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3261.png"
 ALT="${\bf r}_u =
{\bf r} - r  {\bf u}/c$">|; 

$key = q/{{bf{a}+({{bf{b}+{{bf{c})=({{bf{a}+{{bf{b})+{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="${\bf a} +
({\bf b} + {\bf c}) = ({\bf a} + {\bf b}) + {\bf c}$">|; 

$key = q/rho({{bf{r}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$\rho({\bf r}')$">|; 

$key = q/{displaymath}k_{i,y}=k_{r,y}=k_{t,y}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2507.png"
 ALT="\begin{displaymath}
k_{i y} = k_{r y} = k_{t y}.
\end{displaymath}">|; 

$key = q/T(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$T(x, y, z)$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig9.ps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="330" BORDER="0"
 SRC="|."$dir".q|img1906.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig9.ps}}
\end{figure}">|; 

$key = q/displaystyleBox,c,{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2972.png"
 ALT="$\displaystyle \Box  c {\bf A}$">|; 

$key = q/|{{bf{r}|rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="$\vert{\bf r}\vert
\rightarrow\infty$">|; 

$key = q/{displaymath}nabla!cdot!{{bf{E}=frac{rho_f}{epsilon_0,epsilon}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1686.png"
 ALT="\begin{displaymath}
\nabla\!\cdot\!{\bf E} = \frac{\rho_f}{\epsilon_0 \epsilon}.
\end{displaymath}">|; 

$key = q/g^{nu'sigma'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2928.png"
 ALT="$g^{\nu'\sigma'}$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig10.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig10.eps}}
\end{figure}">|; 

$key = q/{displaymath}sigma_T=frac{8,pi}{3},r_e^{,2}=6.65times10^{-29},{{rm{m^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2287.png"
 ALT="\begin{displaymath}
\sigma_T = \frac{8 \pi}{3} r_e^{ 2} = 6.65\times 10^{-29} {\rm m^2}.
\end{displaymath}">|; 

$key = q/{displaymath}(nablatimes{{bf{B})_z,dx,dy=mu_0,j_z,dx,dy,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf B})_z  dx dy = \mu_0  j_z dx dy,
\end{displaymath}">|; 

$key = q/nabla{times}{{bf{E}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1692.png"
 ALT="$\nabla{\times}{\bf E} ={\bf0}$">|; 

$key = q/{displaymath}V_2=R_2,I_2+L_2frac{dI_2}{dt}+M,frac{dI_1}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1926.png"
 ALT="\begin{displaymath}
V_2 = R_2  I_2 + L_2 \frac{d I_2}{dt} + M \frac{d I_1}{dt}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{|{{bf{f}_{{rm{electrical}|}{|{{bf{f}_{{rm{gravitational}|}=fraq_1}{m_1}frac{q_2}{m_2}frac{1}{4pi,epsilon_0,G}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="\begin{displaymath}
\frac{\vert{\bf f}_{\rm electrical}\vert}{\vert{\bf f}_{\rm ...
...\frac{q_1}{m_1}\frac{q_2}{m_2} \frac{1}{4\pi \epsilon_0  G}.
\end{displaymath}">|; 

$key = q/nablatimes{{bf{A}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$\nabla\times{\bf A}= {\bf0}$">|; 

$key = q/{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="${\bf r}$">|; 

$key = q/displaystyle{{bf{E}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2526.png"
 ALT="$\displaystyle {\bf E}_r$">|; 

$key = q/phi=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="$\phi = $">|; 

$key = q/{displaymath}intf({{bf{r}),delta({{bf{r}),d^3{{bf{r}=f({{bf{0}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="\begin{displaymath}
\int f({\bf r})  \delta({\bf r}) d^3{\bf r} =f({\bf0}),
\end{displaymath}">|; 

$key = q/u({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="$u({\bf r})$">|; 

$key = q/displaystylefrac{e}{4pi,epsilon_0,c^3}frac{sintheta}{r},dot{u}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3281.png"
 ALT="$\displaystyle \frac{e}{4\pi \epsilon_0  c^3} \frac{\sin\theta}{r}  \dot{u}.$">|; 

$key = q/I({{bf{r}',t-|{{bf{r}-{{bf{r}'|slashc),dz',hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2208.png"
 ALT="$I({\bf r}', t - \vert{\bf r} - {\bf r}'\vert/c) dz'  \hat{\bf z}$">|; 

$key = q/({{bf{a}cdot{{bf{b})cdot{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$({\bf a}\cdot{\bf b}) \cdot{\bf c}$">|; 

$key = q/{displaymath}M=k,sqrt{L_1,L_2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img1916.png"
 ALT="\begin{displaymath}
M= k  \sqrt{L_1  L_2},
\end{displaymath}">|; 

$key = q/+z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2371.png"
 ALT="$+z$">|; 

$key = q/{displaymath}nablacdot{{bf{B}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="\begin{displaymath}
\nabla \cdot {\bf B} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}left[intnabla!cdot!({{bf{E},phi),d^3{{bf{r}+intE^2,d^3{{bf{r}right]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \left[\int \nabla\!\cdot \!({\bf E} \phi) d^3{\bf r}
+
\int E^2 d^3 {\bf r}\right]
\end{displaymath}">|; 

$key = q/{displaymath}nablatimes{{bf{B}=epsilon_0,mu_0,(epsilon-1),frac{partial{{bf{E}}{pac{epsilon}{c^2},frac{partial{{bf{E}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2314.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} =\epsilon_0 \mu_0 (\epsilon-1) \frac{...
...t}=
\frac{\epsilon}{c^2} \frac{\partial {\bf E}}{\partial t},
\end{displaymath}">|; 

$key = q/-0.98times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1788.png"
 ALT="$-0.98\times 10^{-5}$">|; 

$key = q/{{bf{I}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="${\bf I}'$">|; 

$key = q/{{bf{j}=(j_x,j_y,j_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="${\bf j} = (j_x, j_y, j_z)$">|; 

$key = q/t_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="$t_2$">|; 

$key = q/{displaymath}q(r)=frac{4}{3}pi,r^3,rho,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="\begin{displaymath}
q(r) = \frac{4}{3} \pi  r^3 \rho,
\end{displaymath}">|; 

$key = q/{{bf{e}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="${\bf e}_z$">|; 

$key = q/{displaymath}frac{partialU}{partialt}+nabla!cdot!{{bf{u}=-{{bf{E}!cdot!{{bf{j},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3213.png"
 ALT="\begin{displaymath}
\frac{\partial U}{\partial t} + \nabla\!\cdot \!{\bf u}
= - {\bf E}\!\cdot\!{\bf j},
\end{displaymath}">|; 

$key = q/displaystylenablacdot{{bf{E}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="$\displaystyle \nabla\cdot{\bf E}({\bf r})$">|; 

$key = q/{displaymath}oint_S{{bf{B}cdotd{{bf{l}=int_Snablatimes{{bf{B}cdotd{{bf{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="\begin{displaymath}
\oint_S {\bf B} \cdot d{\bf l} = \int_S \nabla\times {\bf B} \cdot d{\bf S},
\end{displaymath}">|; 

$key = q/{displaymath}d^4x'=d^4x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img2940.png"
 ALT="\begin{displaymath}
d^4 x' = d^4 x
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}times{{bf{c}=-{{bf{b}cdot{{bf{a}times{{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} \times{\bf c} = - {\bf b} \cdot {\bf a} \times{\bf c}.
\end{displaymath}">|; 

$key = q/displaystylefrac{3,epsilon,E_0}{1+2,epsilon}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1750.png"
 ALT="$\displaystyle \frac{3 \epsilon E_0}{1+2 \epsilon}.$">|; 

$key = q/displaystyle{{bf{A}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="$\displaystyle {\bf A}({\bf r})$">|; 

$key = q/{displaymath}nablaf=left(frac{partialf}{partialr},,frac{1}{r}frac{partialf}{partialtheta},,frac{partialf}{partialz}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="\begin{displaymath}
\nabla f = \left(\frac{\partial f}{\partial r}, \frac{1}{r}...
...tial f}{\partial\theta}, \frac{\partial f}{\partial z}\right)
\end{displaymath}">|; 

$key = q/p_{sigma'}^{nu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2926.png"
 ALT="$p_{\sigma'}^{\nu}$">|; 

$key = q/{displaymath}nablaleft(frac{1}{|{{bf{r}-{{bf{r}'|}right)=-nabla'left(frac{1}{|{{bf{r}-{{bf{r}'|}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="\begin{displaymath}
\nabla\left( \frac{1}{\vert{\bf r} - {\bf r}'\vert}\right) = - \nabla'
\left( \frac{1}{\vert{\bf r} - {\bf r}'\vert}\right),
\end{displaymath}">|; 

$key = q/{{bf{curl},{{bf{A}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="${\bf curl} {\bf A} ={\bf0}$">|; 

$key = q/F^{4i}=-E^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3131.png"
 ALT="$F^{4i} = -E^i$">|; 

$key = q/{displaymath}{{bf{E}={{bf{E}_0,{{rm{e}^{-zslashd},{{rm{e}^{,{{rm{i},(k_r,z-omega,t)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2402.png"
 ALT="\begin{displaymath}
{\bf E} = {\bf E}_0 {\rm e}^{-z/d} {\rm e}^{ {\rm i} (k_r z-\omega t)},
\end{displaymath}">|; 

$key = q/q_N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$q_N$">|; 

$key = q/{displaymath}int_{-infty}^{infty}g(x,epsilon),dx=1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} g(x,\epsilon) dx = 1.
\end{displaymath}">|; 

$key = q/q,nA,v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$q n A v$">|; 

$key = q/displaystyle-v_perp,sin({mitOmega},t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="$\displaystyle - v_\perp \sin({\mit\Omega} t),$">|; 

$key = q/{displaymath}A_{k'cdotsl',m'}^{i'cdotsj'}=A_{kcdotsl,m}^{icdotsj},p_i^{i'}cdotspj'}p_{k'}^kcdotsp_{l'}^l,p_{m'}^m+P_1+P_2+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img2825.png"
 ALT="\begin{displaymath}
A_{k'\cdots l', m'}^{i'\cdots j'} = A_{k\cdots l,m}^{i\cdots...
...{j'} p_{k'}^k \cdots p_{l'}^l  p_{m'}^m + P_1 + P_2
+ \cdots,
\end{displaymath}">|; 

$key = q/{mitPhi}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1862.png"
 ALT="${\mit\Phi}_2$">|; 

$key = q/displaystyleV_0,exp({{rm{i},omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2008.png"
 ALT="$\displaystyle V_0  \exp({\rm i} \omega  t),$">|; 

$key = q/z=x+{{rm{i},y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1539.png"
 ALT="$z=x +{\rm i} y$">|; 

$key = q/{{bf{B}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="${\bf B}_0$">|; 

$key = q/{displaymath}{{bf{S}=sum_i{{bf{S}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="\begin{displaymath}
{\bf S} = \sum_i {\bf S}_i.
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{l}=-frac{partial}{partialt}!int_S{{bf{B}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="\begin{displaymath}
\oint_C {\bf E} \cdot d{\bf l} = - \frac{\partial}{\partial t}\! \int_S
{\bf B} \cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/oint_S{{bf{h}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$\oint_S {\bf h}\cdot d{\bf S}$">|; 

$key = q/{displaymath}int!int_S{{bf{v}cdotd{{bf{S}=lim_{dSrightarrow0}left[sumv,costheta,dSright],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="\begin{displaymath}
\int\!\int_S {\bf v}\cdot d{\bf S} = \lim_{dS\rightarrow 0}\left[ \sum v \cos\theta
 dS\right],
\end{displaymath}">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$y$">|; 

$key = q/{displaymath}Z_0=sqrt{frac{L}{C}}=left(frac{mu_0}{4pi^2,epsilon_0}right)^{1slash2}ln,(bslasha)=60,ln,(bslasha),,{{rm{ohms}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2071.png"
 ALT="\begin{displaymath}
Z_0 = \sqrt{\frac{L}{C} } = \left(\frac{\mu_0}{4\pi^2  \eps...
...0}\right)^{1/2}
\ln  (b/a) = 60  \ln  (b/a)   {\rm ohms}.
\end{displaymath}">|; 

$key = q/x_2^mu-x_1^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2879.png"
 ALT="$x_2^\mu-x_1^\mu$">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{l}=int_Snablatimes{{bf{B}cdotd{{bf{S}=mu_0,{calI},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="\begin{displaymath}
\oint_C {\bf B}\cdot d{\bf l} = \int_S \nabla\times{\bf B} \cdot d{\bf S}
= \mu_0  {\cal I},
\end{displaymath}">|; 

$key = q/tantheta_i=beta=n_2slashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2569.png"
 ALT="$\tan\theta_i = \beta = n_2/n_1$">|; 

$key = q/A=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="$A=-1$">|; 

$key = q/int_Vnabla!cdot!{{bf{B},dVneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$\int_V \nabla\!\cdot\! {\bf B}  dV \neq 0 $">|; 

$key = q/{displaymath}int_P^Qleft(f,dx+g,dyright)=int_P^QdF(x,y)=F(Q)-F(P).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{displaymath}
\int_P^Q \left(f dx + g dy\right) = \int_P^Q dF(x,y) = F(Q) - F(P).
\end{displaymath}">|; 

$key = q/G^{44}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3085.png"
 ALT="$G^{44}=0$">|; 

$key = q/{{rm{TM}_{mn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2634.png"
 ALT="${\rm TM}_{mn}$">|; 

$key = q/{displaymath}p=M,x,frac{c}{L}=frac{E}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2142.png"
 ALT="\begin{displaymath}
p = M x  \frac{c}{L} = \frac{E}{c}.
\end{displaymath}">|; 

$key = q/B_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1833.png"
 ALT="$B_c$">|; 

$key = q/partialrslashpartialx=xslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$\partial r/\partial x = x/r$">|; 

$key = q/oint{{bf{v}cdotd{{bf{S}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="$\oint {\bf v}\cdot d{\bf S} = 0$">|; 

$key = q/{displaymath}x=v,t=frac{p}{M}frac{L}{c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2141.png"
 ALT="\begin{displaymath}
x = v  t = \frac{p}{M} \frac{L}{c},
\end{displaymath}">|; 

$key = q/displaystyleepsilon_1,E_{perp,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2496.png"
 ALT="$\displaystyle \epsilon_1 E_{\perp 1}$">|; 

$key = q/epsilon_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1689.png"
 ALT="$\epsilon_2$">|; 

$key = q/{{bf{u}!cdot!dot{{bf{u}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3384.png"
 ALT="${\bf u}\!\cdot \!\dot{\bf u}=0$">|; 

$key = q/U(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1573.png"
 ALT="$U(x,y)$">|; 

$key = q/{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="${\bf b}$">|; 

$key = q/deltatheta_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\delta \theta_x$">|; 

$key = q/partial{{bf{E}slash{partialt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="$\partial {\bf E}/{\partial t}$">|; 

$key = q/{displaymath}frac{partialv_x}{partialx}+frac{partialv_y}{partialy}+frac{partialv_z}{partialz}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="\begin{displaymath}
\frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} +
\frac{\partial v_z}
{\partial z}=0.
\end{displaymath}">|; 

$key = q/partial^2Tslashpartialx^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$\partial^2 T/\partial x^2$">|; 

$key = q/r=-c,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3119.png"
 ALT="$r=-c t$">|; 

$key = q/displaystylez';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle z'$">|; 

$key = q/displaystylefrac{mu_0,e}{4pi}frac{[{{bf{u}]}{[r+{{bf{r}!cdot!{{bf{u}slashc]},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3122.png"
 ALT="$\displaystyle \frac{\mu_0 e}{4\pi}
\frac{[{\bf u}]}{[r+ {\bf r}\!\cdot\!{\bf u}/c]},$">|; 

$key = q/0<theta<pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3374.png"
 ALT="$0&lt;\theta&lt;\pi/2$">|; 

$key = q/{displaymath}{{bf{E}_3={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1452.png"
 ALT="\begin{displaymath}
{\bf E}_3 = {\bf0}
\end{displaymath}">|; 

$key = q/{{bf{E}={{bf{B}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="${\bf E} = {\bf B} = {\bf0}$">|; 

$key = q/displaystyle-frac{E_r}{v_1},hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2549.png"
 ALT="$\displaystyle - \frac{E_r}{v_1} \hat{\bf y},$">|; 

$key = q/{displaymath}|{{bf{r}-z',hat{{bf{z}|simeqr,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2212.png"
 ALT="\begin{displaymath}
\vert{\bf r} - z'  \hat{\bf z}\vert \simeq r,
\end{displaymath}">|; 

$key = q/{displaymath}I(t)=frac{V}{R}+kexp(-R,tslashL).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1897.png"
 ALT="\begin{displaymath}
I(t) = \frac{V}{R} + k \exp(-R t/L).
\end{displaymath}">|; 

$key = q/displaystyle-{{rm{i},frac{partialU}{partialy}+frac{partialV}{partialy}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1556.png"
 ALT="$\displaystyle -{\rm i} \frac{\partial U}{\partial y} + \frac{\partial V}
{\partial y}.$">|; 

$key = q/{{bf{u}=(u_1,u_2,u_3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2753.png"
 ALT="${\bf u}
=(u_1, u_2, u_3)$">|; 

$key = q/{displaymath}epsilon_{pm}=1-frac{omega_p^{,2}}{omega,(omegapm{mitOmega})},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2375.png"
 ALT="\begin{displaymath}
\epsilon_{\pm} = 1 - \frac{\omega_p^{ 2}}{\omega (\omega\pm{\mit \Omega})},
\end{displaymath}">|; 

$key = q/displaystylefrac{mu_0}{4pi}int_{-pislash2}^{pislash2}frac{I,rho}{rho^3,(cosphi)^{-3}}frac{rho}{cos^2phi},dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int_{-\pi/2}^{\pi/2} \frac{I \rho}
{\rho^3  (\cos\phi)^{-3}}\frac{\rho}{\cos^2\phi}  d\phi$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig9.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig9.eps}}
\end{figure}">|; 

$key = q/displaystyle+left[rho,{{bf{E}+{{bf{j}times{{bf{B}right]_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2188.png"
 ALT="$\displaystyle +
\left[\rho {\bf E}+{\bf j}\times {\bf B}\right]_i,$">|; 

$key = q/(0,0,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2696.png"
 ALT="$(0,0,0,0)$">|; 

$key = q/k,lll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2093.png"
 ALT="$k l\ll 1$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig27.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig27.eps}}
\end{figure}">|; 

$key = q/d{{bf{l}=(dx,dy,dz);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$d{\bf l} = (dx,dy,dz)$">|; 

$key = q/C_{ij}=A_{ij}pmB_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2808.png"
 ALT="$C_{ij} = A_{ij} \pm B_{ij}$">|; 

$key = q/{displaymath}{{bf{B}_0=frac{hat{{bf{k}times{{bf{E}_0}{v}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2442.png"
 ALT="\begin{displaymath}
{\bf B}_0 = \frac{\hat{\bf k}\times {\bf E}_0}{v}.
\end{displaymath}">|; 

$key = q/{displaymath}nablaphi={{bf{A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="\begin{displaymath}
\nabla\phi = {\bf A},
\end{displaymath}">|; 

$key = q/oint_S{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$\oint_S {\bf A}\cdot
d{\bf S}$">|; 

$key = q/{displaymath}{{bf{v}=-{{rm{i},omega,{{bf{r}=-frac{{{rm{i},omega,e,{{bf{E}}{m_e,omega,(omega+{{rm{i},nu)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2428.png"
 ALT="\begin{displaymath}
{\bf v} = -{\rm i} \omega {\bf r} = - \frac{{\rm i} \omega e {\bf E}}{m_e \omega (\omega+{\rm i} \nu)}.
\end{displaymath}">|; 

$key = q/usimeqc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3326.png"
 ALT="$u\simeq c$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1610.png"
 ALT="$g$">|; 

$key = q/{displaymath}d=frac{q}{m}frac{E,t^2}{2}=frac{q}{m}frac{E,l^2}{2,v^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="\begin{displaymath}
d = \frac{q}{m} \frac{E t^2}{2} = \frac{q}{m} \frac{E l^2}{2 v^2},
\end{displaymath}">|; 

$key = q/d{{bf{S}=(dS_x,,dS_y,,dS_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$d{\bf S} = (dS_x,  dS_y,  dS_z)$">|; 

$key = q/{displaymath}ds^2=c^2,dtau^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img2931.png"
 ALT="\begin{displaymath}
ds^2 = c^2  d\tau^2.
\end{displaymath}">|; 

$key = q/displaystyleE_{parallel};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2600.png"
 ALT="$\displaystyle E_{\parallel}$">|; 

$key = q/u=(u_1^{~2}+u_2^{~2}+u_3^{~2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2756.png"
 ALT="$u=(u_1^{&nbsp;2} + u_2^{&nbsp;2}+ u_3^{&nbsp;2})^{1/2}$">|; 

$key = q/x'rightarrowx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2717.png"
 ALT="$x'\rightarrow x$">|; 

$key = q/omega_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3393.png"
 ALT="$\omega_0&gt;0$">|; 

$key = q/{displaymath}W=|F|,(|r|,costheta)={{bf{F}cdot{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="\begin{displaymath}
W = \vert F\vert  (\vert r\vert \cos\theta) = {\bf F}\cdot {\bf r}.
\end{displaymath}">|; 

$key = q/partialslashpartialtequiv-{{rm{i},omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2573.png"
 ALT="$\partial/\partial t\equiv -{\rm i} \omega$">|; 

$key = q/{displaymath}{{bf{grad},T=left(frac{partialT}{partialx},,frac{partialT}{partialy},,frac{partialT}{partialz}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="\begin{displaymath}
{\bf grad} T = \left(\frac{\partial T}{\partial x},  \frac{\partial T}{\partial y}, 
\frac{\partial T}{\partial z}\right).
\end{displaymath}">|; 

$key = q/displaystyle-mu_0,j_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$\displaystyle - \mu_0  j_z.$">|; 

$key = q/-q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1523.png"
 ALT="$-q'$">|; 

$key = q/{displaymath}dh=frac{partialh}{partialx},dx+frac{partialh}{partialy},dy,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="\begin{displaymath}
dh = \frac{\partial h}{\partial x}  dx +\frac{\partial h}
{\partial y}  dy,
\end{displaymath}">|; 

$key = q/displaystylerho,tanphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="$\displaystyle \rho \tan\phi,$">|; 

$key = q/displaystyleR_2,I_2+L,frac{dI_2}{dt}+M,frac{dI_1}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1958.png"
 ALT="$\displaystyle R_2  I_2 + L  \frac{d I_2}{d t} + M \frac{d I_1}{dt},$">|; 

$key = q/nabla^2phi_m=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1817.png"
 ALT="$\nabla^2\phi_m=0$">|; 

$key = q/{displaymath}phi(z=0^+)=phi(z=0^-).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1713.png"
 ALT="\begin{displaymath}
\phi(z=0^+) = \phi(z=0^-).
\end{displaymath}">|; 

$key = q/displaystyle-F_{4i}=-E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3035.png"
 ALT="$\displaystyle -F_{4i} = -E_i,$">|; 

$key = q/displaystylephi({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="$\displaystyle \phi({\bf r},t)$">|; 

$key = q/{displaymath}oint_S{{bf{E}cdotd{{bf{S}=oint_SE_r,dS_r=E_r(r),4pi,r^2=frac{q}{4piepsilon_0,r^2},,4pi,r^2=frac{q}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="\begin{displaymath}
\oint_S{\bf E}\cdot d{\bf S}= \oint_S E_r  dS_r = E_r(r)  ...
...q}{4\pi\epsilon_0 r^2}  4\pi  r^2 =
\frac{q}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=left(frac{da_x}{dt},frac{da_y}{dt},frac{da_z}{dt}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \left(\frac{d a_x}{dt}, \frac{d a_y}{d t}, \frac{d a_z}{ d t}\right).
\end{displaymath}">|; 

$key = q/{displaymath}A_z({{bf{r},t)=frac{mu_0}{4pi}int_{-lslash2}^{lslash2}frac{I(z',t-|at{{bf{z}|slashc)}{|{{bf{r}-z',hat{{bf{z}|},dz'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2210.png"
 ALT="\begin{displaymath}
A_z ({\bf r}, t) = \frac{\mu_0}{4\pi} \int_{-l/2}^{l/2}
\fr...
...t{\bf z} \vert/c)}{\vert{\bf r} - z'  \hat{\bf z}\vert} dz'.
\end{displaymath}">|; 

$key = q/{displaymath}c^2-u^2=frac{c^2,(c^2-u'^2),(c^2-v^2)}{(c^2+u'_1,v)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2758.png"
 ALT="\begin{displaymath}
c^2 - u^2 = \frac{c^2  (c^2-u'^2)  (c^2-v^2)}{(c^2 + u'_1  v)^2}.
\end{displaymath}">|; 

$key = q/{T^mu}_nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3197.png"
 ALT="${T^\mu}_\nu$">|; 

$key = q/n,({{bf{a}+{{bf{b})=n,{{bf{a}+n,{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$n ({\bf a} + {\bf b}) = n {\bf a} + n {\bf b}$">|; 

$key = q/N(x+dx,y,z),q,d_x,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1668.png"
 ALT="$N(x+dx,y,z) q d_x dy dz$">|; 

$key = q/{displaymath}oint_S{{bf{E}_3cdotd{{bf{S}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1441.png"
 ALT="\begin{displaymath}
\oint_S {\bf E}_3 \cdot d{\bf S} = 0.
\end{displaymath}">|; 

$key = q/dx=x-x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$dx=x-x_0$">|; 

$key = q/ominus;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="$\ominus$">|; 

$key = q/F(Q);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$F(Q)$">|; 

$key = q/{displaymath}{mitPhi}_1=M,I_2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1923.png"
 ALT="\begin{displaymath}
{\mit\Phi}_1 = M  I_2.
\end{displaymath}">|; 

$key = q/displaystylefrac{rho}{cos^2phi},dphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="$\displaystyle \frac{\rho}{\cos^2\phi}  d\phi,$">|; 

$key = q/(AB);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$(AB)$">|; 

$key = q/displaystyle(x_2'-x_1')^2+(y_2'-y_1')^2+(z_2'-z_1')^2-c^2,(t_2'-t_1')^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2855.png"
 ALT="$\displaystyle (x_2'-x_1')^2 + (y_2'-y_1')^2 + (z_2'-z_1')^2 -c^2 (t_2'-t_1')^2,$">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}times{{bf{c})neq({{bf{a}times{{bf{b})times{{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b} \times{\bf c})\neq ({\bf a}\times{\bf b}) \times{\bf c}.
\end{displaymath}">|; 

$key = q/{displaymath}nablar=-c,nablat'=nabla'r+frac{partialr}{partialt'},nablat'=frac{{{bf{r}}{r}-frac{{{bf{r}!cdot!{{bf{u}}{r},nablat',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3248.png"
 ALT="\begin{displaymath}
\nabla r = - c  \nabla t' = \nabla'r + \frac{\partial r}{ \...
...c{{\bf r}}{r} - \frac{{\bf r}\!\cdot\!{\bf u}}{r}
 \nabla t',
\end{displaymath}">|; 

$key = q/displaystyle+rho,{{bf{E}+{{bf{j}times{{bf{B}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2185.png"
 ALT="$\displaystyle +
\rho {\bf E}+{\bf j}\times {\bf B}.$">|; 

$key = q/{displaymath}V_0=E_0,l.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2254.png"
 ALT="\begin{displaymath}
V_0 = E_0  l.
\end{displaymath}">|; 

$key = q/{displaymath}f_i=-frac{e}{gamma,c},(F_{i4},U^4+F_{ij},U^j),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3173.png"
 ALT="\begin{displaymath}
f_i = -\frac{e}{\gamma c}  (F_{i4}  U^4 + F_{ij}  U^j),
\end{displaymath}">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4piepsilon_0}intfrac{rho({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="\begin{displaymath}
\phi({\bf r} ) = \frac{1}{4\pi \epsilon_0} \int\frac{\rho({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'}.
\end{displaymath}">|; 

$key = q/lim_{,dSrightarrow0}oint{{bf{A}cdotd{{bf{l}slashdS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="$\lim_{ dS\rightarrow 0}\oint{\bf A}\cdot d{\bf l} /dS$">|; 

$key = q/{displaymath}({{bf{a}times{{bf{b})times{{bf{c}=({{bf{a}cdot{{bf{c}),{{bf{b}-({{bf{b}cdot{{bf{c}),{{bf{a}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="\begin{displaymath}
({\bf a}\times{\bf b})\times{\bf c} = ({\bf a}\cdot{\bf c}) {\bf b} -({\bf b}
\cdot{\bf c}) {\bf a}
\end{displaymath}">|; 

$key = q/nablacdot{{bf{E}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="$\nabla\cdot {\bf E}=0$">|; 

$key = q/partial_mu=(nabla,c^{-1}partialslashpartialt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3022.png"
 ALT="$\partial_\mu
=(\nabla, c^{-1} \partial/\partial t)$">|; 

$key = q/r'=sqrt{x^{'2}+y^{'2}+z^{'2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3107.png"
 ALT="$r'=\sqrt{x^{'2}+y^{'2}+z^{'2}}$">|; 

$key = q/{displaymath}P^mu=m_0,U^mu=gamma,m_0,({{bf{u},c)=({{bf{p},Eslashc),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3164.png"
 ALT="\begin{displaymath}
P^\mu = m_0  U^\mu = \gamma  m_0  ({\bf u}, c) = ({\bf p}, E/c),
\end{displaymath}">|; 

$key = q/v(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1479.png"
 ALT="$v(x)$">|; 

$key = q/displaystylec,A_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3111.png"
 ALT="$\displaystyle c A_2$">|; 

$key = q/x_2equivy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2174.png"
 ALT="$x_2\equiv y$">|; 

$key = q/{displaymath}V=int_{y_1}^{y_2}dyleft[int_{x_1(y)}^{x_2(y)}D(x,y),dxright]equivint!int_SD(x,y),dx,dy.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="\begin{displaymath}
V = \int_{y_1}^{y_2} dy\left[\int_{x_1(y)}^{x_2(y)} D(x,y) dx\right]
\equiv \int\!\int_S D(x,y) dx dy.
\end{displaymath}">|; 

$key = q/A_i^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2816.png"
 ALT="$A_i^i$">|; 

$key = q/{displaymath}R_{{rm{rad}=frac{P_{{rm{rad}}{I_0^{,2}slash2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2235.png"
 ALT="\begin{displaymath}
R_{\rm rad} = \frac{P_{\rm rad}}{I_0^{ 2}/2},
\end{displaymath}">|; 

$key = q/p^{mu'}_{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2939.png"
 ALT="$p^{\mu'}_{\mu}$">|; 

$key = q/B_perp=mu,H_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1820.png"
 ALT="$B_\perp=\mu H_\perp$">|; 

$key = q/displaystylep_i^{i'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2783.png"
 ALT="$\displaystyle p_i^{i'},$">|; 

$key = q/displaystylenablaV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1567.png"
 ALT="$\displaystyle \nabla V$">|; 

$key = q/{displaymath}{{bf{a}'simeq{{bf{a}+deltambox{{boldmath{{theta{}times{{bf{a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="\begin{displaymath}
{\bf a}' \simeq {\bf a} + \delta \mbox{\boldmath$\theta$}\times {\bf a},
\end{displaymath}">|; 

$key = q/{displaymath}v_p=frac{c}{sqrt{1-omega_p^{,2}slashomega^{2}}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2334.png"
 ALT="\begin{displaymath}
v_p = \frac{c}{\sqrt{1-\omega_p^{ 2}/\omega^{2}}},
\end{displaymath}">|; 

$key = q/S'(x',y',z',t');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2652.png"
 ALT="$S'(x',y',z',t')$">|; 

$key = q/displaystyle~_{lim|deltax|rightarrow0}frac{U(x+deltax,y)+{{rm{i},V(x+deltax,y)-U(x,y)-{{rm{i},V(x,y)}{deltax};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1552.png"
 ALT="$\displaystyle&nbsp;_{\lim \vert\delta x\vert\rightarrow 0}
\frac{U(x+\delta x, y) + {\rm i}  V(x+\delta x, y) - U(x, y) - {\rm i} 
V(x,y)}{\delta x}$">|; 

$key = q/dz';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2663.png"
 ALT="$dz'$">|; 

$key = q/rho_b=-nabla!cdot!{{bf{P};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1722.png"
 ALT="$\rho_b = - \nabla\!\cdot\!
{\bf P}$">|; 

$key = q/C_{kl}^j=A_{ikl}^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2814.png"
 ALT="$C_{kl}^j = A_{ikl}^{ij}$">|; 

$key = q/d{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$d{\bf S}$">|; 

$key = q/{displaymath}left.epsilon,frac{partialphi}{partialr}right|_{r=a+}=left.frac{partialphi}{partialr}right|_{r=a-}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1748.png"
 ALT="\begin{displaymath}
\left.\epsilon \frac{\partial \phi}{\partial r}\right\vert ...
...} = \left.
\frac{\partial\phi}{\partial r}\right\vert _{r=a-}.
\end{displaymath}">|; 

$key = q/displaystyleU(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1543.png"
 ALT="$\displaystyle U(x, y)$">|; 

$key = q/{displaymath}z=frac{e,E_0}{m_e,(omega^2-omega_0^{,2})}sin(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2300.png"
 ALT="\begin{displaymath}
z = \frac{e E_0}{m_e (\omega^2-\omega_0^{ 2})} \sin(\omega t).
\end{displaymath}">|; 

$key = q/Vsim1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="$V \sim 1$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="$m$">|; 

$key = q/displaystylegamma,({{bf{B}_perp-{{bf{v}times{{bf{E}slashc^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3100.png"
 ALT="$\displaystyle \gamma ({\bf B}_\perp-{\bf v}\times{\bf E}/c^2),$">|; 

$key = q/I_0=omega,q_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2202.png"
 ALT="$I_0 = \omega  q_0$">|; 

$key = q/(b,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1521.png"
 ALT="$(b, 0,  0)$">|; 

$key = q/{displaymath}nablatimes{{bf{E}={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="\begin{displaymath}
\nabla\times {\bf E} = {\bf0}
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig42.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="615" HEIGHT="215" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig42.eps}}
\end{figure}">|; 

$key = q/c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2147.png"
 ALT="$c^2$">|; 

$key = q/{displaymath}p=frac{epsilon_0}{2},E^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="\begin{displaymath}
p = \frac{\epsilon_0}{2}  E^2.
\end{displaymath}">|; 

$key = q/displaystyle0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1600.png"
 ALT="$\displaystyle 0$">|; 

$key = q/{displaymath}g=frac{U}{c}=frac{|{{bf{u}|}{c^2}=frac{epsilon_0,E^2}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2145.png"
 ALT="\begin{displaymath}
g = \frac{U}{c}= \frac{\vert{\bf u}\vert}{c^2} = \frac{\epsilon_0  E^2}{c}.
\end{displaymath}">|; 

$key = q/d{mitOmega}=sintheta,dtheta,dvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2266.png"
 ALT="$d{\mit\Omega} = \sin\theta d\theta d\varphi$">|; 

$key = q/{displaymath}{{bf{B}=nablatimes{{bf{A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="\begin{displaymath}
{\bf B} = \nabla\times{\bf A},
\end{displaymath}">|; 

$key = q/qslashm=1.759times10^{11}~{{rm{C,kg^{-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$q/m = 1.759\times 10^{11}&nbsp;{\rm C  kg^{-1}}$">|; 

$key = q/lsimlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2241.png"
 ALT="$l\sim \lambda$">|; 

$key = q/displaystylefrac{dv_x}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$\displaystyle \frac{dv_x}{dt}$">|; 

$key = q/{displaymath}F_{ij}=partial_i{mitPhi}_j-partial_j{mitPhi}_i=-c,B_{ij}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3033.png"
 ALT="\begin{displaymath}
F_{ij} = \partial_i{\mit\Phi}_j -\partial_j{\mit\Phi}_i= - c  B_{ij}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{dvarphi}{dz}={mitDelta}k=frac{omega_p^{,2},{mitOmega}}{2,omega}{2,epsilon_0,m_e^{,2},c}frac{n_e,B_0}{omega^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2387.png"
 ALT="\begin{displaymath}
\frac{d\varphi}{dz} = {\mit\Delta}k = \frac{\omega_p^{ 2} ...
...ac{e^3}{2 \epsilon_0 m_e^{ 2} c}\frac{n_e B_0}{\omega^2}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{A}_1({{bf{r})=frac{mu_0}{4pi}int_{{rm{all,space}frac{{{bf{j}({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1874.png"
 ALT="\begin{displaymath}
{\bf A}_1({\bf r}) = \frac{\mu_0}{4\pi} \int_{\rm all  spac...
...bf j}({\bf r}')}
{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r}',
\end{displaymath}">|; 

$key = q/muggmu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1798.png"
 ALT="$\mu\gg \mu_0$">|; 

$key = q/|{{bf{F}|rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$\vert{\bf F}\vert\rightarrow 0$">|; 

$key = q/-{{bf{f};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="$-{\bf f}$">|; 

$key = q/U>c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2764.png"
 ALT="$U&gt;c$">|; 

$key = q/theta_{{rm{max}rightarrowpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3349.png"
 ALT="$\theta_{\rm max} \rightarrow \pi/2$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig48.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img2446.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig48.eps}}
\end{figure}">|; 

$key = q/hat{{bf{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2126.png"
 ALT="$\hat{\bf k}$">|; 

$key = q/{displaymath}phi({{bf{r},t)simeqfrac{l}{4pi,epsilon_0,c}frac{z}{r}frac{I(t-rslashc)}{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2222.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) \simeq \frac{l}{4\pi \epsilon_0  c} \frac{z}{r} \frac{I(t-r/c)}{r}.
\end{displaymath}">|; 

$key = q/{displaymath}partial^muA^{nusigma}equivg^{mutau}{A^{nusigma}}_{,tau}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2910.png"
 ALT="\begin{displaymath}
\partial^\mu A^{\nu\sigma} \equiv g^{\mu\tau} {A^{\nu\sigma}}_{,\tau}.
\end{displaymath}">|; 

$key = q/{{bf{I}'=q,nA,{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="${\bf I}' = q nA {\bf v}$">|; 

$key = q/{displaymath}{{bf{p}=m,{{bf{u},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img3162.png"
 ALT="\begin{displaymath}
{\bf p} = m  {\bf u},
\end{displaymath}">|; 

$key = q/displaystyleepsilon_0mu_0,frac{partial^2{{bf{A}}{partialt^2}-nabla^2{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="$\displaystyle \epsilon_0\mu_0 \frac{\partial^2{\bf A} }{\partial t^2} -
\nabla^2{\bf A}$">|; 

$key = q/arightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$a\rightarrow\infty$">|; 

$key = q/displaystylefrac{E_i}{v_1},{{rm{e}^{,{{rm{i},(k_1,z-omega,t)},hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2452.png"
 ALT="$\displaystyle \frac{E_i}{v_1} {\rm e}^{ {\rm i} (k_1 z-\omega t)} \hat{\bf y},$">|; 

$key = q/displaystyleu_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2729.png"
 ALT="$\displaystyle u_1$">|; 

$key = q/{displaymath}r_e=frac{e^2}{4pi,epsilon_0,m_e,c^2}=2.82times10^{-15},{{rm{m}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2285.png"
 ALT="\begin{displaymath}
r_e = \frac{e^2}{4\pi \epsilon_0 m_e c^2} = 2.82\times 10^{-15} {\rm m}
\end{displaymath}">|; 

$key = q/displaystyleF_x[,k,(r-c,t),],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$\displaystyle F_x [ k (r-c t) ],$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig8.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="283" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig8.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{V(0,t)}{I(0,t)}=R.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2080.png"
 ALT="\begin{displaymath}
\frac{V(0,t)}{I(0,t)} = R.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig25.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="228" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig25.eps}}
\end{figure}">|; 

$key = q/3times10^7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="$3\times 10^7$">|; 

$key = q/{displaymath}-epsilon_0,frac{partial{{bf{E}}{partialt}times{{bf{B}-epsilon_0,{{bs(nablatimes{{bf{B})}{mu_0}+{{bf{j}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2178.png"
 ALT="\begin{displaymath}
-\epsilon_0 \frac{\partial {\bf E}}{\partial t}\times {\bf ...
...}\times(\nabla\times {\bf B})}{\mu_0} + {\bf j}\times {\bf B}.
\end{displaymath}">|; 

$key = q/int{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="$\int {\bf A}\cdot d{\bf S}$">|; 

$key = q/nablatimes{{bf{W};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="$\nabla\times{\bf W}$">|; 

$key = q/int_P^Q{{bf{grad},Tcdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$\int_P^Q {\bf grad } T\cdot d{\bf l}$">|; 

$key = q/{displaymath}nablat'=-frac{{{bf{r}}{s,c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3249.png"
 ALT="\begin{displaymath}
\nabla t' = - \frac{{\bf r}}{s c},
\end{displaymath}">|; 

$key = q/{displaymath}P_i=I_i,frac{d{mitPhi}_i}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1981.png"
 ALT="\begin{displaymath}
P_i = I_i  \frac{d {\mit\Phi}_i}{dt}.
\end{displaymath}">|; 

$key = q/displaystylephi(x,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1598.png"
 ALT="$\displaystyle \phi(x, 0)$">|; 

$key = q/{displaymath}|langle{{bf{u}rangle|=frac{c,epsilon_0,E_0^{,2}}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2279.png"
 ALT="\begin{displaymath}
\vert\langle {\bf u}\rangle\vert = \frac{c \epsilon_0 E_0^{ 2}}{2}.
\end{displaymath}">|; 

$key = q/{displaymath}k^2=frac{omega^2}{c^2}+{{rm{i},frac{omega_p^{,2},omega}{nu,c^2}=mu_0,omega,(epsilon_0,omega+{{rm{i},sigma).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="293" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2437.png"
 ALT="\begin{displaymath}
k^2 = \frac{\omega^2}{c^2} + {\rm i} \frac{\omega_p^{ 2} ...
...,c^2} = \mu_0 \omega (\epsilon_0 \omega + {\rm i} \sigma).
\end{displaymath}">|; 

$key = q/{displaymath}int_P^Q=left.int_1^2y^3,dxright|_{y=0}+left.int_0^1x,dyright|_{x=2}=2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="\begin{displaymath}
\int_P^Q = \left.\int_1^2 y^3 dx\right\vert _{y=0} + \left.\int_0^1 x dy\right\vert _{x=2} = 2.
\end{displaymath}">|; 

$key = q/(r,theta,varphi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1730.png"
 ALT="$(r, \theta, \varphi)$">|; 

$key = q/n_e(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2388.png"
 ALT="$n_e(z)$">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="$D$">|; 

$key = q/T(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$T(x)$">|; 

$key = q/omega=2pi,f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="$\omega = 2\pi f$">|; 

$key = q/phi_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1819.png"
 ALT="$\phi_m$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intleft(frac{{{bf{j}times{{bf{R}}{R^3}-frac{1}{2}frac^2{{bf{j}slashpartialt^2)times{{bf{R}}{c^2R}+cdotsright),dV'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi} \int \left(\frac{{\bf j}\times{\bf R}}{R^3} - ...
...{(\partial^2 {\bf j}/ \partial t^2)\times{\bf R}}{c^2 R} +\cdots \right) d V'.$">|; 

$key = q/{displaymath}{{bf{E}_0cdot{{bf{B}_0=frac{{{bf{E}_0cdot{{bf{k}times{{bf{E}_0}{omega}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="\begin{displaymath}
{\bf E}_0 \cdot {\bf B}_0 = \frac{
{\bf E}_0 \cdot {\bf k} \times {\bf E}_0 }{ \omega }= 0.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partialV}{partialx}=A_x,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="\begin{displaymath}
\frac{\partial V}{\partial x} = A_x,
\end{displaymath}">|; 

$key = q/e^2slash(6pi,epsilon_0,m_e,c^2)=1.28times10^{-15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3328.png"
 ALT="$e^2/(6\pi \epsilon_0 m_e  c^2)
= 1.28\times 10^{-15}$">|; 

$key = q/displaystylefrac{m,pi}{b},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2615.png"
 ALT="$\displaystyle \frac{m \pi}{b},$">|; 

$key = q/{displaymath}phi={{rm{constant}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2643.png"
 ALT="\begin{displaymath}
\phi = {\rm constant}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{E}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="\begin{displaymath}
{\bf f} = q  {\bf E}.
\end{displaymath}">|; 

$key = q/{displaymath}nabla(phi,psi)=phi,nablapsi+psi,nablaphi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="\begin{displaymath}
\nabla(\phi \psi) =\phi \nabla\psi+\psi \nabla\phi
\end{displaymath}">|; 

$key = q/displaystylefrac{partial}{partialx_j}!left[epsilon_0,E^2,delta_{ij}slash2-epsilon_0,E_i,E_j+B^2,delta_{ij}slash2,mu_0-B_i,B_jslashmu_0right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2187.png"
 ALT="$\displaystyle \frac{\partial}{\partial x_j}\!\left[\epsilon_0 E^2 \delta_{ij}/2 - \epsilon_0 E_i E_j+ B^2 \delta_{ij}/2 \mu_0 - B_i B_j/\mu_0\right]$">|; 

$key = q/{bf{r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\bf r$">|; 

$key = q/{displaymath}intT^4,dS_4+intT^{4'},dS_{4'}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3290.png"
 ALT="\begin{displaymath}
\int T^4 dS_4 + \int T^{4'} dS_{4'} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{r}=(x,,y,,z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="\begin{displaymath}
{\bf r} = (x,  y,  z),
\end{displaymath}">|; 

$key = q/int_P^Q{{bf{A}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$\int_P^Q {\bf A}\cdot d{\bf l}$">|; 

$key = q/dx'^2+dy'^2+dz'^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2682.png"
 ALT="$dx'^2+dy'^2 + dz'^2$">|; 

$key = q/{displaymath}Boxpsi=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2980.png"
 ALT="\begin{displaymath}
\Box \psi = 0.
\end{displaymath}">|; 

$key = q/V(x,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2044.png"
 ALT="$V(x, t)$">|; 

$key = q/displaystyleint_0^T(R_1,I_1^{,2}+R_2,I_2^{,2}),dt+frac{1}{2},L_1,I_1^{,2}+frac{1}{2},L_2,I_2^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1961.png"
 ALT="$\displaystyle \int_0^T (R_1  I_1^{ 2} + R_2  I_2^{ 2}) dt +\frac{1}{2}  L_1  I_1^{ 2}
+ \frac{1}{2}  L_2  I_2^{ 2}$">|; 

$key = q/displaystyleE_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2602.png"
 ALT="$\displaystyle E_z$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}=frac{e^2,dot{u}^2}{16pi^2,epsilon_0,c^3}fpha,cosphi]^2}{[1-(uslashc),sinalpha,cosphi]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="506" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3370.png"
 ALT="\begin{displaymath}
\frac{d P(t')}{d{\mit\Omega}} = \frac{e^2  \dot{u}^2}{16\pi...
...-\sin\alpha \cos\phi]^2}
{[1-(u/c) \sin\alpha \cos\phi]^5}.
\end{displaymath}">|; 

$key = q/displaystyleE_y(z=0^+);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1702.png"
 ALT="$\displaystyle E_y (z=0^+)$">|; 

$key = q/displaystylephi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3105.png"
 ALT="$\displaystyle \phi'$">|; 

$key = q/{displaymath}frac{dE}{dt}=f,u=m_0,gamma^3,u,frac{du}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3159.png"
 ALT="\begin{displaymath}
\frac{dE}{dt} = f u = m_0  \gamma^3  u  \frac{du}{dt}.
\end{displaymath}">|; 

$key = q/H_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1811.png"
 ALT="$H_\parallel$">|; 

$key = q/nablacdot{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$\nabla\cdot {\bf E}$">|; 

$key = q/{{bf{r}_u={{bf{r}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3269.png"
 ALT="${\bf r}_u = {\bf r}_0$">|; 

$key = q/P^mu=(d{{bf{p},dEslashc);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3309.png"
 ALT="$P^\mu = (d{\bf p}, dE/c)$">|; 

$key = q/Q=(a,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$Q=(a,0,0)$">|; 

$key = q/{displaymath}P(t')=-frac{dE}{dt'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3338.png"
 ALT="\begin{displaymath}
P(t') = - \frac{dE}{dt'},
\end{displaymath}">|; 

$key = q/|a|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\vert a\vert=0$">|; 

$key = q/{displaymath}{{bf{H}=frac{{bf{B}{mu_0}-{{bf{M}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1782.png"
 ALT="\begin{displaymath}
{\bf H} = \frac{\bf B}{\mu_0} - {\bf M}
\end{displaymath}">|; 

$key = q/E_{y,1}=E_{y,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2534.png"
 ALT="$E_{y 1} = E_{y 2}$">|; 

$key = q/{displaymath}(nablatimes{{bf{A})_r=frac{1}{r,sintheta}frac{partial(sintheta,A_phc{1}{r,sintheta}frac{partialA_theta}{partialphi}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf A})_r = \frac{1}{r \sin\theta}\frac{\part...
...-\frac{1}{r \sin\theta}\frac{\partial A_\theta}{\partial\phi}
\end{displaymath}">|; 

$key = q/displaystylenabla^2phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1400.png"
 ALT="$\displaystyle \nabla^2 \phi_1$">|; 

$key = q/{displaymath}nabla=nabla'-frac{{{bf{r}}{s,c}frac{partial}{partialt'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3250.png"
 ALT="\begin{displaymath}
\nabla = \nabla' - \frac{{\bf r}}{s c} \frac{\partial}{\partial t'}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a},&,{{bf{b}=a_x,b_y+a_y,b_z+a_z,b_x={{rm{scalar~number},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="368" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="\begin{displaymath}
{\bf a} \&amp; {\bf b} = a_x  b_y + a_y  b_z + a_z  b_x = {\rm scalar&nbsp;number},
\end{displaymath}">|; 

$key = q/partialslashpartialt'|_{x^i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3241.png"
 ALT="$\partial/\partial t'\vert _{x^i}$">|; 

$key = q/displaystyle|V_0|,exp({{rm{i},omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2023.png"
 ALT="$\displaystyle \vert V_0\vert  \exp({\rm i} \omega t),$">|; 

$key = q/{{bf{j}({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="${\bf j}({\bf r}, t)$">|; 

$key = q/{displaymath}frac{1}{X}frac{d^2X}{dx^2}=-frac{1}{Y}frac{d^2Y}{dy^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1608.png"
 ALT="\begin{displaymath}
\frac{1}{X}\frac{d^2 X}{d x^2} = - \frac{1}{Y} \frac{d^2 Y}{d y^2}.
\end{displaymath}">|; 

$key = q/{{bf{P}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1672.png"
 ALT="${\bf P}({\bf r})$">|; 

$key = q/phirightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="$\phi\rightarrow 0$">|; 

$key = q/r_0=e^2slash(4pi,epsilon_0,m_0,c^2)=2.82times10^{-15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3386.png"
 ALT="$r_0 = e^2/(4\pi \epsilon_0  m_0  c^2) = 2.82\times 10^{-15}$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1796.png"
 ALT="$\mu$">|; 

$key = q/displaystyleepsilon_0left[nabla(E^2slash2)-(nablacdot{{bf{E}),{{bf{E}-({{bf{E}cdotnabla){{bf{E}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2183.png"
 ALT="$\displaystyle \epsilon_0\left[\nabla(E^2/2) - (\nabla\cdot {\bf E}) {\bf E} - ({\bf E}\cdot\nabla){\bf E}\right]$">|; 

$key = q/{displaymath}frac{1}{c^2}frac{partialphi}{partialt}+nablacdot{{bf{A}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="\begin{displaymath}
\frac{1}{c^2} \frac{\partial\phi}{\partial t} +\nabla\cdot{\bf A} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}phi({{bf{r})rightarrow0mbox{hspace{1cm}as~~{|{{bf{r}|rightarrowinfty{}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="\begin{displaymath}
\phi({\bf r}) \rightarrow 0\mbox{\hspace{1cm}as&nbsp;&nbsp;$\vert{\bf r}\vert\rightarrow \infty$}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitdiv},{{bf{A}=nablacdot{{bf{A}=frac{partialA_x}{partialx}+frac{partialA_y}{partialy}+frac{partialA_z}{partialz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="\begin{displaymath}
{\mit div} {\bf A} = \nabla\cdot {\bf A} = \frac{\partial A...
...rac{\partial A_y}{\partial y}+\frac{\partial A_z}{\partial z}.
\end{displaymath}">|; 

$key = q/displaystyleE_{parallel,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2462.png"
 ALT="$\displaystyle E_{\parallel 2},$">|; 

$key = q/{displaymath}x^2+y^2+z^2=a^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1528.png"
 ALT="\begin{displaymath}
x^2+y^2+z^2 = a^2.
\end{displaymath}">|; 

$key = q/{displaymath}B_theta=frac{mu_0,I}{2pi,r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="\begin{displaymath}
B_\theta = \frac{\mu_0  I}{2\pi  r}
\end{displaymath}">|; 

$key = q/displaystyleI(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2009.png"
 ALT="$\displaystyle I(t)$">|; 

$key = q/pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1575.png"
 ALT="$\pm 1$">|; 

$key = q/displaystyle{{bf{E}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2530.png"
 ALT="$\displaystyle {\bf E}_t$">|; 

$key = q/10^{42};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$10^{42}$">|; 

$key = q/{displaymath}P(t')=frac{e^2,dot{u}^2}{8pi,epsilon_0,c^3}int_0^pifrac{sin^3theta,{-1}^{+1}frac{(1-mu^2),dmu}{[1-(uslashc),mu]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="541" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3352.png"
 ALT="\begin{displaymath}
P(t')= \frac{e^2 \dot{u}^2}{8\pi  \epsilon_0  c^3} \int_0...
...,c^3}
\int_{-1}^{+1} \frac{(1-\mu^2) d\mu}{[1-(u/c) \mu]^5}.
\end{displaymath}">|; 

$key = q/{displaymath}nablaf=left(frac{partialf}{partialr},,frac{1}{r}frac{partialf}{partc{1}{r,sintheta}frac{partialf}{partialphi}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="\begin{displaymath}
\nabla f = \left(\frac{\partial f}{\partial r}, \frac{1}{r}...
...,\frac{1}{r \sin\theta}\frac{\partial f}{\partial\phi}\right)
\end{displaymath}">|; 

$key = q/E^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3071.png"
 ALT="$E^{ij}$">|; 

$key = q/Arightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$A\rightarrow 0$">|; 

$key = q/displaystyle{{bf{E}({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="$\displaystyle {\bf E}({\bf r}, t)$">|; 

$key = q/{displaymath}costheta=frac{{{bf{a}cdot{{bf{b}}{|a|,|b|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="\begin{displaymath}
\cos\theta = \frac{{\bf a} \cdot {\bf b}}{\vert a\vert  \vert b\vert }.
\end{displaymath}">|; 

$key = q/E=10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="$E=10^4$">|; 

$key = q/{displaymath}V=I,R+L,frac{dI}{dt}+left.int_0^tI,dtrightslashC.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2006.png"
 ALT="\begin{displaymath}
V = I R+ L \frac{dI}{dt} + \left.\int_0^t I dt\right/C.
\end{displaymath}">|; 

$key = q/llllambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2216.png"
 ALT="$l\ll \lambda$">|; 

$key = q/{mitdiv},({{bf{grad},T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="${\mit div} ({\bf grad} T)$">|; 

$key = q/{displaymath}W=frac{1}{2}int_V{{bf{A}cdot{{bf{j},dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1991.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \int_V {\bf A} \cdot {\bf j}   dV,
\end{displaymath}">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$r$">|; 

$key = q/l=lambdaslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2242.png"
 ALT="$l = \lambda/2$">|; 

$key = q/varphi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2393.png"
 ALT="$\varphi_0$">|; 

$key = q/B_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1470.png"
 ALT="$B_3$">|; 

$key = q/{{bf{M}=N{{bf{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1768.png"
 ALT="${\bf M} = N {\bf m}$">|; 

$key = q/delta_j^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2787.png"
 ALT="$\delta_j^i$">|; 

$key = q/{displaymath}-frac{partial}{partialt}!int_Vrho,dV=oint_S{{bf{j}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2108.png"
 ALT="\begin{displaymath}
-\frac{\partial}{\partial t}\!\int_V \rho d V = \oint_S {\bf j}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/displaystyle{{rm{i},frac{omega}{c^2},E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2583.png"
 ALT="$\displaystyle {\rm i} \frac{\omega}{c^2} E_x$">|; 

$key = q/x_1equivx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2173.png"
 ALT="$x_1 \equiv x$">|; 

$key = q/{displaymath}{mitPhi}_2=M_{21},I_1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1867.png"
 ALT="\begin{displaymath}
{\mit\Phi}_2 = M_{21} I_1,
\end{displaymath}">|; 

$key = q/xrightarrow-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="$x\rightarrow -x$">|; 

$key = q/{displaymath}epsilon_0mu_0,frac{partial^2phi}{partialt^2}-nabla^2phi=frac{rho}{epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="\begin{displaymath}
\epsilon_0\mu_0 \frac{\partial^2\phi}{\partial t^2} - \nabla^2\phi = \frac{\rho}
{\epsilon_0}.
\end{displaymath}">|; 

$key = q/i=j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2193.png"
 ALT="$i=j$">|; 

$key = q/dx^2+dy^2+dz^2-c^2,dt^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2688.png"
 ALT="$dx^2 + dy^2 + dz^2 -c^2  dt^2$">|; 

$key = q/displaystyle+frac{sigma}{2epsilon_0}mbox{hspace{2cm}below}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="$\displaystyle +\frac{\sigma}{2\epsilon_0} \mbox{\hspace{2cm} below}.$">|; 

$key = q/displaystylemu_0,{{bf{j}+epsilon_0,mu_0,frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2313.png"
 ALT="$\displaystyle \mu_0 {\bf j}+ \epsilon_0 \mu_0 \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/{displaymath}frac{partialA^{nusigma}}{partialx^{mu}}={A^{nusigma}}_{,mu}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2905.png"
 ALT="\begin{displaymath}
\frac{\partial A^{\nu\sigma}}{\partial x^{\mu}} = {A^{\nu\sigma}}_{,\mu}.
\end{displaymath}">|; 

$key = q/{displaymath}P(t')=frac{e^2}{6pi,epsilon_0,c^3},gamma^4,dot{u}^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3383.png"
 ALT="\begin{displaymath}
P(t') = \frac{e^2}{6\pi \epsilon_0  c^3} \gamma^4 \dot{u}^2,
\end{displaymath}">|; 

$key = q/displaystyleepsilon^{ijk},epsilon_{iab};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3006.png"
 ALT="$\displaystyle \epsilon^{ijk}  \epsilon_{iab}$">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}intE^2,d^3{{bf{r}=frac{1}{2}sum_{i=1}^Nq_i,phi_i+sum_{i=1}^NW_i{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \int E^2  d^3{\bf r} = \frac{1}{2} \sum_{i=1}^N
q_i  \phi_i + \sum_{i=1}^N W_i
\end{displaymath}">|; 

$key = q/displaystyleleft(-nabla^2+frac{1}{c^2}frac{partial^2}{partialt^2}right){{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2969.png"
 ALT="$\displaystyle \left(-\nabla^2+\frac{1}{c^2} \frac{\partial^2}{\partial t^2}\right){\bf A}$">|; 

$key = q/{displaymath}frac{partialr}{partialt}=cleft(1-frac{partialt'}{partialt}right)=frf{r}!cdot!{{bf{u}}{r},frac{partialt'}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3245.png"
 ALT="\begin{displaymath}
\frac{\partial r}{\partial t} = c\left(1-\frac{\partial t'}{...
...{{\bf r}\!\cdot\!{\bf u}}{r}  \frac{\partial t'}{\partial t},
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intleft([rho]nabla(R^{-1})+frac{[partialrhoslashpartialt]}{R},nablat_rright),dV';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$\displaystyle \frac{1}{4\pi \epsilon_0}\int \left(
[\rho] \nabla(R^{-1}) + \frac{[\partial\rho/\partial t]}{R}  \nabla t_r\right) dV'$">|; 

$key = q/{displaymath}frac{partial,nablacdot{{bf{B}}{partialt}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="\begin{displaymath}
\frac{\partial  \nabla\cdot{\bf B}}{\partial t} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2phi=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2642.png"
 ALT="\begin{displaymath}
\nabla^2\phi = 0.
\end{displaymath}">|; 

$key = q/{displaymath}frac{dsigma}{d{mitOmega}}=r_e^{,2},sin^2theta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2284.png"
 ALT="\begin{displaymath}
\frac{d\sigma}{d{\mit\Omega}} = r_e^{ 2} \sin^2\theta,
\end{displaymath}">|; 

$key = q/{displaymath}U=frac{1}{2},{{bf{E}!cdot!{{bf{D}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1765.png"
 ALT="\begin{displaymath}
U = \frac{1}{2}  {\bf E}\!\cdot\!{\bf D}.
\end{displaymath}">|; 

$key = q/{displaymath}int_P^Q{{bf{A}cdotd{{bf{l}=V(Q),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="\begin{displaymath}
\int_P^Q {\bf A}\cdot d{\bf l} = V(Q),
\end{displaymath}">|; 

$key = q/{displaymath}P=frac{e^2}{6pi,epsilon_0,c^3},gamma^4,dot{u}^2=frac{e^2}{6pi,epsilon_0,c^3}frac{gamma^4,u^4}{rho^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3330.png"
 ALT="\begin{displaymath}
P = \frac{e^2}{6\pi \epsilon_0  c^3}  
\gamma^4  \dot{u}...
...ac{e^2}{6\pi \epsilon_0  c^3} \frac{\gamma^4  u^4}{\rho^2},
\end{displaymath}">|; 

$key = q/{displaymath}B_theta=frac{mu_0,I}{2pi,r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="\begin{displaymath}
B_\theta = \frac{\mu_0 I}
{2 \pi  r},
\end{displaymath}">|; 

$key = q/displaystyleepsilon_0,E^iE_j+frac{B^iB_j}{mu_0}-delta_j^i,frac{1}{2}!left(epsilon_0,E^kE_k+frac{B^kB_k}{mu_0}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3199.png"
 ALT="$\displaystyle \epsilon_0  E^i E_j + \frac{B^i B_j}{\mu_0}
- \delta_j^i \frac{1}{2} \! \left(\epsilon_0 E^k E_k +\frac{B^k B_k}{\mu_0}\right),$">|; 

$key = q/{{bf{a}cdot{{bf{b}times{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="${\bf a}\cdot {\bf b}\times {\bf c}$">|; 

$key = q/{displaymath}F=frac{mu_0,I_1,I_2}{2pi,r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="\begin{displaymath}
F= \frac{\mu_0  I_1  I_2}{2\pi  r}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_S{{bf{A}cdotd{{bf{S}=int_V{mitdiv},{{bf{A},,dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="\begin{displaymath}
\oint_S {\bf A}\cdot d{\bf S} = \int_V {\mit div} {\bf A}  dV,
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_perp';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3099.png"
 ALT="$\displaystyle {\bf B}_\perp'$">|; 

$key = q/displaystyleleft(frac{n_1-n_2}{n_1+n_2}right)E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2473.png"
 ALT="$\displaystyle \left(\frac{n_1-n_2}{n_1+n_2}\right) E_i,$">|; 

$key = q/gamma(u),V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2955.png"
 ALT="$\gamma(u)  V$">|; 

$key = q/{displaymath}oint_Srho,{{bf{v}cdotd{{bf{S}=-frac{partial}{partialt}!left(int_Vrho,,dVright){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="\begin{displaymath}
\oint_S \rho {\bf v}\cdot d{\bf S} = -\frac{\partial}{\partial t}\!\left(
\int_V \rho   dV\right)
\end{displaymath}">|; 

$key = q/i,j,k,cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2774.png"
 ALT="$i,j,k,\cdots$">|; 

$key = q/{displaymath}mbox{{boldmath{{rho{}=a,(cosphi,,sinphi,,0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3356.png"
 ALT="\begin{displaymath}
\mbox{\boldmath$\rho$}= a (\cos\phi,  \sin\phi,  0),
\end{displaymath}">|; 

$key = q/displaystyle+Mint_0^Tleft(I_1,frac{dI_2}{dt}+I_2,frac{dI_1}{dt}right),dt.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1962.png"
 ALT="$\displaystyle + M \int_0^T \left(I_1  \frac{dI_2}{dt} + I_2 \frac{d I_1}{dt } \right) dt.$">|; 

$key = q/{displaymath}{mitdiv},(rho,{{bf{v})=-frac{partialrho}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="\begin{displaymath}
{\mit div} (\rho {\bf v}) = -\frac{\partial \rho}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}I=intA_nu,Q^{4nu},d^3x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3300.png"
 ALT="\begin{displaymath}
I = \int A_\nu  Q^{4\nu}  d^3 x
\end{displaymath}">|; 

$key = q/displaystyleBox^2{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="$\displaystyle \Box^2 {\bf A}$">|; 

$key = q/{displaymath}nablacdot{{bf{j}=-frac{partialrho}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf j} = -\frac{\partial \rho}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}dh={{bf{grad},hcdotd{{bf{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="\begin{displaymath}
dh = {\bf grad} h \cdot d{\bf l}.
\end{displaymath}">|; 

$key = q/{displaymath}partial_muT^{munu}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3307.png"
 ALT="\begin{displaymath}
\partial_\mu T^{\mu\nu} = 0,
\end{displaymath}">|; 

$key = q/PQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2992.png"
 ALT="$PQ$">|; 

$key = q/3times10^{14};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3329.png"
 ALT="$3\times 10^{14}$">|; 

$key = q/{displaymath}oint_Snablatimes{{bf{B}cdotd{{bf{S}=mu_0,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="\begin{displaymath}
\oint_S \nabla\times {\bf B} \cdot d{\bf S} = \mu_0  I.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{E}=frac{rho}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf E} = \frac{\rho}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{{bf{F}=-{{bf{r}slash|r^3|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="${\bf F} = - {\bf r}/ \vert r^3\vert$">|; 

$key = q/{displaymath}phi_3={{rm{constant}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1417.png"
 ALT="\begin{displaymath}
\phi_3 = {\rm constant}
\end{displaymath}">|; 

$key = q/exp[{{rm{i},phi(k)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2339.png"
 ALT="$\exp[{\rm i} \phi(k)]$">|; 

$key = q/J^mu=({{bf{j},rho,c);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3048.png"
 ALT="$J^\mu = ({\bf j}, \rho  c)$">|; 

$key = q/{displaymath}{{bf{g}=frac{{bf{u}{c^2}=epsilon_0,{{bf{E}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3222.png"
 ALT="\begin{displaymath}
{\bf g} = \frac{\bf u}{c^2} = \epsilon_0  {\bf E}\times{\bf B}.
\end{displaymath}">|; 

$key = q/dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$dx$">|; 

$key = q/displaystylefrac{u_2}{gamma,(1-u_1,vslashc^2)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2748.png"
 ALT="$\displaystyle \frac{u_2}{\gamma (1-u_1  v/c^2)},$">|; 

$key = q/{displaymath}left(frac{partialr}{partialt'}right)_{x^i}=-frac{{{bf{r}!cdot!{{bf{u}}{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img3244.png"
 ALT="\begin{displaymath}
\left(\frac{\partial r}{\partial t'}\right)_{x^i} = - \frac{{\bf r}\!\cdot
\!{\bf u}}{r}.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}frac{V^2}{d^2},A,d=frac{1}{2},C,V^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="\begin{displaymath}
W = \frac{\epsilon_0}{2} \frac{V^2}{d^2}  A  d= \frac{1}{2}  C  V^2,
\end{displaymath}">|; 

$key = q/{displaymath}phi(z<0)=frac{1}{4pi,epsilon_0,epsilon_2}frac{q''}{R_1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1711.png"
 ALT="\begin{displaymath}
\phi(z&lt;0) = \frac{1}{4\pi \epsilon_0 \epsilon_2} \frac{q''}{R_1}.
\end{displaymath}">|; 

$key = q/{displaymath}P_{{rm{rad}=frac{omega^2,l^2,I_0^{,2}}{12pi,epsilon_0,c^3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2232.png"
 ALT="\begin{displaymath}
P_{\rm rad} = \frac{\omega^2  l^2  I_0^{ 2}}{12\pi  \epsilon_0  c^3}.
\end{displaymath}">|; 

$key = q/(nablatimes{{bf{B})_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="$(\nabla\times{\bf B})_z=0$">|; 

$key = q/{displaymath}oint_C{{bf{A}cdotd{{bf{l}=int_S{{bf{curl,A}cdotd{{bf{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="\begin{displaymath}
\oint_C {\bf A} \cdot d{\bf l} = \int_S {\bf curl  A}\cdot d{\bf S},
\end{displaymath}">|; 

$key = q/{displaymath}|{{bf{r}-{{bf{r'}|=c,(t-t').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="\begin{displaymath}
\vert{\bf r} - {\bf r'}\vert = c (t-t').
\end{displaymath}">|; 

$key = q/{{bf{D}=epsilon_0,{{bf{E}+{{bf{P};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1780.png"
 ALT="${\bf D} = \epsilon_0 {\bf E} +
{\bf P}$">|; 

$key = q/bslasha=3.38,exp(sqrt{epsilon});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2097.png"
 ALT="$b/a = 3.38 \exp(\sqrt{\epsilon})$">|; 

$key = q/y=y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2704.png"
 ALT="$y=y'$">|; 

$key = q/dlll;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$d\ll l$">|; 

$key = q/epsilon_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1688.png"
 ALT="$\epsilon_1$">|; 

$key = q/{displaymath}P=N,q,V=I,V{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="\begin{displaymath}
P = N q V = I V
\end{displaymath}">|; 

$key = q/displaystyleleft(sintheta_i,,0,,-costheta_iright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2519.png"
 ALT="$\displaystyle \left(\sin\theta_i, 0, -\cos\theta_i\right),$">|; 

$key = q/ssimeqr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3273.png"
 ALT="$s\simeq r$">|; 

$key = q/{displaymath}int_VE_3^{~2},dV=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1450.png"
 ALT="\begin{displaymath}
\int_V E_3^{&nbsp;2}  dV =0.
\end{displaymath}">|; 

$key = q/{displaymath}A_{i'j'cdotsk'}=A_{ijcdotsk},p_{i'}^i,p_{j'}^jcdotsp_{k'}^k.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img2792.png"
 ALT="\begin{displaymath}
A_{i'j'\cdots k'} = A_{ij\cdots k}  p_{i'}^i  p_{j'}^j \cdots p_{k'}^k.
\end{displaymath}">|; 

$key = q/{displaymath}L_1=mu_0,N_1^{,2},pi,r^2,l,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1913.png"
 ALT="\begin{displaymath}
L_1 = \mu_0  N_1^{ 2}  \pi  r^2  l,
\end{displaymath}">|; 

$key = q/{displaymath}E_r(r)=frac{Q}{4pi,epsilon_0,r^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="\begin{displaymath}
E_r(r) = \frac{Q}{4\pi \epsilon_0 r^2}
\end{displaymath}">|; 

$key = q/E_t=E_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2477.png"
 ALT="$E_t=E_i$">|; 

$key = q/ullc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3271.png"
 ALT="$u\ll c$">|; 

$key = q/{displaymath}int_a^bf_n(x),f_m(x),dx=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1643.png"
 ALT="\begin{displaymath}
\int_a^b f_n(x)  f_m(x)  dx = 0,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{curl},{{bf{A}=nablatimes{{bf{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="\begin{displaymath}
{\bf curl} {\bf A} = \nabla\times {\bf A}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial}{partialx'}=left(frac{partialx}{partialx'}right)_{y',zpartialx'}right)_{y',z'}frac{partial}{partialz},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="433" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial x'} = \left(\frac{\partial x}{\part...
...l z}{\partial x'} \right)_{y',z'}
\frac{\partial}{\partial z},
\end{displaymath}">|; 

$key = q/A_mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3298.png"
 ALT="$A_\mu$">|; 

$key = q/displaystyle8.8542times10^{-12},{{rm{C}^2,{{rm{N}^{-1},{{rm{m}^{-2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="$\displaystyle 8.8542\times 10^{-12}  {\rm C}^2 {\rm N}^{-1} {\rm m}^{-2},$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G=-4pi,F(t-t'),delta({{bf{r}-{{bf{r}').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right)
G = - 4\pi  F(t-t') \delta({\bf r}- {\bf r}').
\end{displaymath}">|; 

$key = q/v_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="$v_1$">|; 

$key = q/{displaymath}delta_j^i,p_i^{i'},p_{j'}^j=p_{j}^{i'},p_{j'}^j=delta_{j'}^{i'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img2805.png"
 ALT="\begin{displaymath}
\delta_j^i  p_i^{i'} p_{j'}^j = p_{j}^{i'}  p_{j'}^j = \delta_{j'}^{i'}.
\end{displaymath}">|; 

$key = q/x^2+y^2<c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1588.png"
 ALT="$x^2+y^2&lt; c^2$">|; 

$key = q/aa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="$aa$">|; 

$key = q/{displaymath}phi(z=0)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1486.png"
 ALT="\begin{displaymath}
\phi(z=0) = 0,
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot({{bf{E},phi)=phi,nabla!cdot!{{bf{E}+{{bf{E}!cdot!nablaphi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="\begin{displaymath}
\nabla \cdot({\bf E}  \phi) = \phi \nabla\!\cdot\!{\bf E} +{\bf E}\! \cdot\!
\nabla\phi.
\end{displaymath}">|; 

$key = q/{displaymath}sintheta_r=sintheta_i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2513.png"
 ALT="\begin{displaymath}
\sin\theta_r = \sin\theta_i,
\end{displaymath}">|; 

$key = q/{displaymath}partial_muQ^{munu}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3297.png"
 ALT="\begin{displaymath}
\partial_\mu Q^{\mu\nu}=0,
\end{displaymath}">|; 

$key = q/displaystylefrac{1-epsilon}{1+2,epsilon},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1749.png"
 ALT="$\displaystyle \frac{1-\epsilon}{1+2 \epsilon},$">|; 

$key = q/displaystyle{{bf{E}_0cos,({{bf{k}cdot{{bf{r}-omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$\displaystyle {\bf E}_0 \cos ({\bf k}\cdot {\bf r} - \omega  t),$">|; 

$key = q/displaystyleepsilon_0mu_0,frac{partial^2phi}{partialt^2}-nabla^2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="$\displaystyle \epsilon_0\mu_0 \frac{\partial^2\phi}{\partial t^2} - \nabla^2\phi$">|; 

$key = q/(x^{1'},x^{2'},cdots,x^{n'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2779.png"
 ALT="$(x^{1'}, x^{2'}, \cdots, x^{n'})$">|; 

$key = q/displaystyle-frac{partial}{partialt}!int_S{{bf{B}cdotd{{bf{S},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="$\displaystyle - \frac{\partial }{\partial t}\!
\int_S {\bf B}\cdot d{\bf S},$">|; 

$key = q/R^mu=({{bf{r},c,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2896.png"
 ALT="$R^\mu = ({\bf r}, c t)$">|; 

$key = q/t<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2005.png"
 ALT="$t&lt;0$">|; 

$key = q/displaystylelangle{{bf{u}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2151.png"
 ALT="$\displaystyle \langle {\bf u}\rangle$">|; 

$key = q/epsilon^{ijk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3002.png"
 ALT="$\epsilon^{ijk}$">|; 

$key = q/{displaymath}G^{munu}=frac{1}{2},epsilon^{munualphabeta}F_{alphabeta}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3059.png"
 ALT="\begin{displaymath}
G^{\mu\nu} = \frac{1}{2}  \epsilon^{\mu\nu\alpha\beta} F_{\alpha\beta}.
\end{displaymath}">|; 

$key = q/{displaymath}dT={{bf{grad},Tcdotd{{bf{l}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="\begin{displaymath}
dT = {\bf grad} T \cdot d{\bf l} = 0.
\end{displaymath}">|; 

$key = q/s_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2365.png"
 ALT="$s_\pm$">|; 

$key = q/{displaymath}omega_{11}=c,pi,sqrt{frac{1}{a^2}+frac{1}{b^2}}>omega_{10}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2636.png"
 ALT="\begin{displaymath}
\omega_{11} = c \pi \sqrt{\frac{1}{a^2}+\frac{1}{b^2}}&gt;\omega_{10}.
\end{displaymath}">|; 

$key = q/{displaymath}phi(z>0)=frac{1}{4pi,epsilon_0,epsilon_1}left(frac{q}{R_1}+frac{q'}{R_2}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1706.png"
 ALT="\begin{displaymath}
\phi(z&gt;0) = \frac{1}{4\pi \epsilon_0  \epsilon_1}\left(\frac{q}{R_1}
+ \frac{q'}{R_2}\right),
\end{displaymath}">|; 

$key = q/{displaymath}k=left.{{rm{i},sqrt{omega_p^{,2}-omega^2}rightslashc={{rm{i},|k|.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img2348.png"
 ALT="\begin{displaymath}
k = \left.{\rm i} \sqrt{\omega_p^{ 2}-\omega^2}\right/c = {\rm i} \vert k\vert.
\end{displaymath}">|; 

$key = q/displaystylemu_0,{{bf{j},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle \mu_0 {\bf j},$">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}times{{bf{c})equiv({{bf{a}cdot{{bf{c}),{{bf{b}-({{bf{a}cdot{{bf{b}),{{bf{c}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b} \times {\bf c}) \equiv ({\bf a}\cdot {\bf c})  {\bf b} - ({\bf a}\cdot
{\bf b}) {\bf c}
\end{displaymath}">|; 

$key = q/J^mu=e,n_0,U^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3186.png"
 ALT="$J^\mu = e  n_0  U^\mu$">|; 

$key = q/displaystylefrac{rho}{epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1428.png"
 ALT="$\displaystyle \frac{\rho}{\epsilon_0}$">|; 

$key = q/{displaymath}P=I,V=I^2,R=frac{V^2}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="\begin{displaymath}
P = I V = I^2  R = \frac{V^2}{R}.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fresnel.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="767" HEIGHT="332" BORDER="0"
 SRC="|."$dir".q|img2563.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fresnel.eps}}
\end{figure}">|; 

$key = q/{displaymath}g_{mu'nu'},p_{musigma}^{mu'}p_{nu}^{nu'}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2925.png"
 ALT="\begin{displaymath}
g_{\mu'\nu'}  p_{\mu\sigma}^{\mu'} p_{\nu}^{\nu'} =0.
\end{displaymath}">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$\lambda$">|; 

$key = q/{displaymath}t=t'+frac{|{{bf{r}-{{bf{r'}|}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="\begin{displaymath}
t = t' +\frac{ \vert{\bf r} - {\bf r'}\vert}{c}.
\end{displaymath}">|; 

$key = q/{displaymath}epsilon_2,nabla!cdot!{{bf{E}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1697.png"
 ALT="\begin{displaymath}
\epsilon_2 \nabla\!\cdot\!{\bf E} = 0
\end{displaymath}">|; 

$key = q/{displaymath}nabla!cdot!{{bf{D}=rho_f,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1678.png"
 ALT="\begin{displaymath}
\nabla\!\cdot\!{\bf D} = \rho_f,
\end{displaymath}">|; 

$key = q/dl=sqrt{2},dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$dl= \sqrt{2}  dx$">|; 

$key = q/V=pi,r^2,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1974.png"
 ALT="$V = \pi  r^2  l$">|; 

$key = q/-0.50times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1793.png"
 ALT="$-0.50\times 10^{-8}$">|; 

$key = q/{displaymath}E_r=frac{q}{2pi,epsilon_0,r}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1388.png"
 ALT="\begin{displaymath}
E_r = \frac{q}{2\pi \epsilon_0 r}
\end{displaymath}">|; 

$key = q/x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$x_2$">|; 

$key = q/displaystylefrac{epsilon-1}{epsilon+2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1741.png"
 ALT="$\displaystyle \frac{\epsilon-1}{\epsilon+2},$">|; 

$key = q/{displaymath}dT={{bf{grad},Tcdotd{{bf{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="\begin{displaymath}
dT = {\bf grad} T \cdot d{\bf l}.
\end{displaymath}">|; 

$key = q/k_i=k_r=omegaslashv_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2510.png"
 ALT="$k_i=k_r = \omega/v_1$">|; 

$key = q/displaystylefrac{1}{4pi}intfrac{C_x({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="$\displaystyle \frac{1}{4\pi } \int\frac{C_x({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'},$">|; 

$key = q/displaystyleq';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1718.png"
 ALT="$\displaystyle q'$">|; 

$key = q/{displaymath}epsilon_1,frac{partialphi(z=0^+)}{partialz}=epsilon_2,frac{partialphi(z=0^-)}{partialz}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1714.png"
 ALT="\begin{displaymath}
\epsilon_1  \frac{\partial\phi(z=0^+)}{\partial z} = \epsilon_2 
\frac{\partial \phi(z=0^-)}{\partial z}.
\end{displaymath}">|; 

$key = q/{displaymath}F=frac{epsilon_0}{2},E_perp^{~2},A=frac{1}{2}frac{C,V^2}{d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="\begin{displaymath}
F = \frac{\epsilon_0}{2}  E_\perp^{&nbsp;2} A= \frac{1}{2} \frac{C  V^2}{d}.
\end{displaymath}">|; 

$key = q/dV'equivd^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="$dV' \equiv d^3{\bf r}'$">|; 

$key = q/{displaymath}frac{da_x}{dt}=frac{d}{dt}!left(phi,b_xright)=frac{dphi}{dt},b_x+phi,frac{db_x}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="\begin{displaymath}
\frac{d a_x}{dt} = \frac{d}{dt}\!\left(\phi  b_x\right) = \frac{d\phi}{dt}  b_x + \phi  
\frac{d b_x}{dt},
\end{displaymath}">|; 

$key = q/{displaymath}deltaW=intnabla!cdot!(phi,delta{{bf{D}),d^3{{bf{r}-intnablaphi!cdot!delta{{bf{D},d^3{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1757.png"
 ALT="\begin{displaymath}
\delta W = \int \nabla\!\cdot\!(\phi \delta{\bf D}) d^3{\bf r}
- \int \nabla\phi\!\cdot\!\delta{\bf D} d^3{\bf r},
\end{displaymath}">|; 

$key = q/{displaymath}langle{{bf{u}rangle=frac{omega^4,p_0^{,2}}{32pi^2,epsilon_0,c^3}frac{sin^2theta}{r^2},hat{{bf{r},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2265.png"
 ALT="\begin{displaymath}
\langle {\bf u}\rangle = \frac{\omega^4 p_0^{ 2}}{32\pi^2 \epsilon_0 c^3}\frac{\sin^2\theta}{r^2} \hat{\bf r},
\end{displaymath}">|; 

$key = q/r^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2000.png"
 ALT="$r^{-3}$">|; 

$key = q/nablatimes{{bf{H}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1814.png"
 ALT="$\nabla\times{\bf H} = {\bf0}$">|; 

$key = q/displaystylepartial_muF^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3089.png"
 ALT="$\displaystyle \partial_\mu F^{\mu\nu}$">|; 

$key = q/C,deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2049.png"
 ALT="$C \delta x$">|; 

$key = q/displaystylet';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2657.png"
 ALT="$\displaystyle t'$">|; 

$key = q/phi({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1396.png"
 ALT="$\phi({\bf r})$">|; 

$key = q/displaystyleW_z({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="$\displaystyle W_z({\bf r} )$">|; 

$key = q/partialTslashpartialxequiv(partialTslashpartialx)_{y,z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\partial T/\partial x\equiv (\partial T/\partial x)_{y, z}$">|; 

$key = q/{{bf{a},&,{{bf{b}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="${\bf a} \&amp; {\bf b}= 1$">|; 

$key = q/{displaymath}V=-M,frac{dI_2}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1924.png"
 ALT="\begin{displaymath}
V = - M  \frac{dI_2}{dt}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_i,{{rm{e}^{,{{rm{i},({{bf{k}_icdot{{bf{r}-omega,t)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2495.png"
 ALT="$\displaystyle {\bf B}_i {\rm e}^{ {\rm i} ({\bf k}_i\cdot{\bf r}-\omega t)},$">|; 

$key = q/E_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2605.png"
 ALT="$E_z=0$">|; 

$key = q/v<c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2760.png"
 ALT="$v&lt;c$">|; 

$key = q/{displaymath}epsilon_0=8.8542times10^{-12},,{{rm{C^{,2},N^{-1}m^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="\begin{displaymath}
\epsilon_0 = 8.8542\times 10^{-12}   {\rm C^{ 2}  N^{-1}m^{-2}}.
\end{displaymath}">|; 

$key = q/q,V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="$q V$">|; 

$key = q/{displaymath}E_r(r)=frac{q}{4pi,epsilon_0,r^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="\begin{displaymath}
E_r (r) = \frac{q}{4\pi \epsilon_0 r^2},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=frac{e}{4pi,epsilon_0}frac{1-u^2slashc^2}{s^3},{{bf{r}_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3268.png"
 ALT="\begin{displaymath}
{\bf E} = \frac{e}{4\pi \epsilon_0} \frac{1-u^2/c^2}{s^3} {\bf r}_0.
\end{displaymath}">|; 

$key = q/g^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2834.png"
 ALT="$g^{ij}$">|; 

$key = q/G^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3223.png"
 ALT="$G^{ij}$">|; 

$key = q/A^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2775.png"
 ALT="$A^{ij}$">|; 

$key = q/{displaymath}{{bf{B}=mu_0,({{bf{H}+{{bf{M}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1803.png"
 ALT="\begin{displaymath}
{\bf B} = \mu_0 ({\bf H} + {\bf M})
\end{displaymath}">|; 

$key = q/(x_2,y_2,z_2,t_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2857.png"
 ALT="$(x_2, y_2, z_2, t_2)$">|; 

$key = q/t_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="$t_1$">|; 

$key = q/{displaymath}nabla^2G=frac{partial^2G}{partialx^2}+frac{partial^2G}{partialy^2}+|,c^2}=frac{1}{c^2}frac{partial^2G}{partialt^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="\begin{displaymath}
\nabla^2 G = \frac{\partial^2 G}{\partial x^2} + \frac{\part...
...vert 
c^2} = \frac{1}{c^2} \frac{\partial^2 G}{\partial t^2},
\end{displaymath}">|; 

$key = q/A,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="$A d$">|; 

$key = q/oint{{bf{E}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="$\oint {\bf E}\cdot d{\bf l}$">|; 

$key = q/deltatheta_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\delta \theta_z$">|; 

$key = q/{displaymath}{{bf{j}({{bf{r},t)=intintdelta({{bf{r}-{{bf{r}')delta(t-t'),{{bf{j}({{bf{r}',t'),d^3{{bf{r}'dt'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="\begin{displaymath}
{\bf j} ({\bf r}, t) = \int\int \delta({\bf r} - {\bf r}') \delta(t-t')  
{\bf j} ({\bf r}', t') d^3 {\bf r}' dt'.
\end{displaymath}">|; 

$key = q/partialslashpartialtequiv0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="$\partial/\partial t \equiv 0$">|; 

$key = q/delta({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$\delta({\bf r})$">|; 

$key = q/displaystylefrac{1}{epsilon_0}int_Vrho,dV,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$\displaystyle \frac{1}{\epsilon_0}\int_V \rho dV,$">|; 

$key = q/D_{perp,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1691.png"
 ALT="$D_{\perp 1}$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0sum_{i=1}^NI_i,delta(x-x_i),delta(y-y_i),hat{{bf{z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0\sum_{i=1}^N I_i  \delta(x-x_i) \delta(y-y_i)
 \hat{\bf z}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial}{partialx'}=costheta,frac{partial}{partialx}+sintheta,frac{partial}{partialy},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial x'} = \cos\theta  \frac{\partial}{\partial x} +
\sin\theta  \frac{\partial}{\partial y},
\end{displaymath}">|; 

$key = q/cslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2328.png"
 ALT="$c/n$">|; 

$key = q/{{bf{E}=-nablaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="${\bf E} = -
\nabla\phi$">|; 

$key = q/oint;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$\oint$">|; 

$key = q/{displaymath}0=L,frac{dI}{dt}+RI,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1951.png"
 ALT="\begin{displaymath}
0 = L \frac{dI}{dt} + RI,
\end{displaymath}">|; 

$key = q/j_z(x,y),dx,dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$j_z(x,y) dx dy$">|; 

$key = q/u^i=u_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2877.png"
 ALT="$u^i=u_i$">|; 

$key = q/{displaymath}nablatimes{{bf{E}=-frac{partial{{bf{B}}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2121.png"
 ALT="\begin{displaymath}
\nabla\times{\bf E} = - \frac{\partial {\bf B}}{\partial t},
\end{displaymath}">|; 

$key = q/deltaW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1856.png"
 ALT="$\delta W$">|; 

$key = q/{{bf{a}equiv(a_x,a_y,a_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="${\bf a} \equiv (a_x, a_y, a_z)$">|; 

$key = q/dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2985.png"
 ALT="$dV$">|; 

$key = q/x=l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2056.png"
 ALT="$x=l$">|; 

$key = q/dA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1877.png"
 ALT="$dA$">|; 

$key = q/{displaymath}frac{dphi}{dk}=x-frac{domega}{dk},t=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2341.png"
 ALT="\begin{displaymath}
\frac{d\phi}{dk} = x - \frac{d\omega}{dk} t = 0.
\end{displaymath}">|; 

$key = q/displaystylenabla!cdot!{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2312.png"
 ALT="$\displaystyle \nabla\!\cdot\!{\bf B}$">|; 

$key = q/{{bf{p}=-p_0,sin(omega,t),hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2301.png"
 ALT="${\bf p} = - p_0 \sin(\omega t) \hat{\bf z}$">|; 

$key = q/f_mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3185.png"
 ALT="$f_\mu$">|; 

$key = q/{displaymath}int_{-infty}^{infty}delta(x),dx=1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} \delta (x) dx = 1.
\end{displaymath}">|; 

$key = q/oint_Srho,{{bf{v}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\oint_S\rho  {\bf v} \cdot d{\bf S}$">|; 

$key = q/{displaymath}dx^2+dy^2+dz^2-c^2,dt^2=K,(dx'^2+dy'^2+dz'^2-c^2,dt'^2),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2686.png"
 ALT="\begin{displaymath}
dx^2 + dy^2 + dz^2 -c^2  dt^2 = K (dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2),
\end{displaymath}">|; 

$key = q/{displaymath}G_{munu}=leftlgrouparray{{cccc}0&-E_z&+E_y&+c,B_x[0.5ex]+E_z&0&-E_xz[0.5ex]-c,B_x&-c,B_y&-c,B_z&0array{rightrgroup.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="111" BORDER="0"
 SRC="|."$dir".q|img3079.png"
 ALT="\begin{displaymath}
G_{\mu\nu} = \left\lgroup \begin{array}{cccc}
0 &amp; -E_z &amp; +E_...
....5ex]
-c B_x &amp; -c B_y &amp;-c B_z &amp; 0\end{array}\right
\rgroup.
\end{displaymath}">|; 

$key = q/{displaymath}I(t)=frac{dq}{dt}=I_0,cos(omega,t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2201.png"
 ALT="\begin{displaymath}
I(t) = \frac{dq}{dt} = I_0  \cos(\omega  t),
\end{displaymath}">|; 

$key = q/n_1neqn_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2478.png"
 ALT="$n_1\neq n_2$">|; 

$key = q/displaystyle(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2-c^2,(t_2-t_1)^2=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2854.png"
 ALT="$\displaystyle (x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2 -c^2 (t_2-t_1)^2
=$">|; 

$key = q/{{bf{r}'={{bf{r}_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="${\bf r}' = {\bf r}_\ast$">|; 

$key = q/Lslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2140.png"
 ALT="$L/c$">|; 

$key = q/displaystyle{{bf{E}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3126.png"
 ALT="$\displaystyle {\bf E}'$">|; 

$key = q/{{bf{u}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2735.png"
 ALT="${\bf u}'$">|; 

$key = q/v_2=cslashn_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2459.png"
 ALT="$v_2=c/n_2$">|; 

$key = q/I_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$I_2$">|; 

$key = q/{displaymath}int{{bf{E}'!cdot!(nablatimes{{bf{H}),d^3{{bf{r}=intfrac{(nablatimes!cdot!frac{partial{{bf{B}}{partialt},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1855.png"
 ALT="\begin{displaymath}
\int {\bf E}'\!\cdot\!(\nabla\times{\bf H}) d^3{\bf r}
= \i...
...bf H}\!\cdot\!\frac{\partial{\bf B}}{\partial t}
 d^3{\bf r}.
\end{displaymath}">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="$b$">|; 

$key = q/0leqkleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1917.png"
 ALT="$0\leq k \leq 1$">|; 

$key = q/{displaymath}lsimfrac{1}{n_e,sigma_T}sim1,{{rm{cm}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2294.png"
 ALT="\begin{displaymath}
l \sim \frac{1}{n_e \sigma_T}\sim 1 {\rm cm}.
\end{displaymath}">|; 

$key = q/displaystyleE_x(z=0^+);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1700.png"
 ALT="$\displaystyle E_x (z=0^+)$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$x$">|; 

$key = q/theta>pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3345.png"
 ALT="$\theta&gt;\pi/2$">|; 

$key = q/{displaymath}{{bf{grad},phi=nablaphi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="\begin{displaymath}
{\bf grad} \phi = \nabla \phi
\end{displaymath}">|; 

$key = q/r+dr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="$r+dr$">|; 

$key = q/x=y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$x=y$">|; 

$key = q/Z_{1slash4}=sqrt{Z_0,Z_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2099.png"
 ALT="$Z_{1/4} = \sqrt{Z_0  Z_1}$">|; 

$key = q/{displaymath}mu_0=4pitimes10^{-7},{{rm{N,A^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="\begin{displaymath}
\mu_0 = 4\pi \times 10^{-7} {\rm N A^{-2}}.
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{E}cdotd{{bf{l}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="\begin{displaymath}
\oint_C {\bf E}\cdot d{\bf l} = 0
\end{displaymath}">|; 

$key = q/nablaphi_3=-{{bf{E}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1446.png"
 ALT="$\nabla\phi_3 = -{\bf E}_3$">|; 

$key = q/displaystyleleft(frac{partialU}{partialx},frac{partialU}{partialy}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1566.png"
 ALT="$\displaystyle \left( \frac{\partial U}{\partial x}, \frac{\partial U}{\partial y}
\right),$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)u=v,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right)u = v,
\end{displaymath}">|; 

$key = q/displaystyleF_{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3034.png"
 ALT="$\displaystyle F_{i4}$">|; 

$key = q/{displaymath}int_0^pisin(n,y),sin(n',y),,dy=frac{pi}{2},delta_{nn'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1631.png"
 ALT="\begin{displaymath}
\int_0^\pi \sin( n y)  \sin (n' y)  dy = \frac{\pi}{2}  \delta_{n n'},
\end{displaymath}">|; 

$key = q/displaystyle0mbox{hspace{2.8cm}otherwise}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="$\displaystyle 0 \mbox{\hspace{2.8cm} otherwise}.$">|; 

$key = q/displaystyleu_3';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2740.png"
 ALT="$\displaystyle u_3'$">|; 

$key = q/displaystyleT^{44};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3210.png"
 ALT="$\displaystyle T^{44}$">|; 

$key = q/{displaymath}p=sigma,E_{{rm{ext}=frac{sigma^2}{2,epsilon_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="\begin{displaymath}
p = \sigma  E_{\rm ext} = \frac{\sigma^2}{2 \epsilon_0}.
\end{displaymath}">|; 

$key = q/k_2=omegaslashv_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2460.png"
 ALT="$k_2=\omega/v_2$">|; 

$key = q/displaystyleq''&=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1720.png"
 ALT="$\displaystyle q''&amp;=$">|; 

$key = q/omega_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2346.png"
 ALT="$\omega_p$">|; 

$key = q/{displaymath}phi({{bf{r})=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="\begin{displaymath}
\phi({\bf r}) = \frac{1}{4\pi \epsilon_0}
\int \frac{ \rho({\bf r}')}{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{displaymath}omega_{10}=frac{c,pi}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img2628.png"
 ALT="\begin{displaymath}
\omega_{10} = \frac{c \pi}{a}.
\end{displaymath}">|; 

$key = q/displaystylefrac{3,E_0}{epsilon+2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1743.png"
 ALT="$\displaystyle \frac{3 E_0}{\epsilon+2}.$">|; 

$key = q/{displaymath}nablatimes{{bf{A}={{rm{i},{{bf{k}times{{bf{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="\begin{displaymath}
\nabla\times{\bf A} = {\rm i}  {\bf k} \times{\bf A}.
\end{displaymath}">|; 

$key = q/displaystyleE_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2472.png"
 ALT="$\displaystyle E_r$">|; 

$key = q/{displaymath}P^mu=frac{1}{c}intT^{4mu},d^3x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3308.png"
 ALT="\begin{displaymath}
P^\mu = \frac{1}{c}\int T^{4\mu} d^3 x
\end{displaymath}">|; 

$key = q/{displaymath}({{bf{a}times{{bf{b})times{{bf{c}equiv({{bf{a}cdot{{bf{c}),{{bf{b}-({{bf{b}cdot{{bf{c}),{{bf{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{displaymath}
({\bf a}\times{\bf b}) \times {\bf c}\equiv ({\bf a}\cdot {\bf c})  {\bf b} - ({\bf b}\cdot
{\bf c}) {\bf a}.
\end{displaymath}">|; 

$key = q/icdotsj;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2796.png"
 ALT="$i\cdots j$">|; 

$key = q/displaystyleV_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1957.png"
 ALT="$\displaystyle V_2$">|; 

$key = q/dE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3311.png"
 ALT="$dE$">|; 

$key = q/{displaymath}{{bf{E}=-frac{e,gamma}{4pi,epsilon_0,{r'}^3}{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img3138.png"
 ALT="\begin{displaymath}
{\bf E} = -\frac{e \gamma}{4\pi \epsilon_0 {r'}^3} {\bf r}.
\end{displaymath}">|; 

$key = q/theta_r=theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2514.png"
 ALT="$\theta_r=\theta_i$">|; 

$key = q/{displaymath}partial^muequivfrac{partial}{partialx_mu}=left(-nabla,frac{1}{c}frac{partial}{partialt}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2909.png"
 ALT="\begin{displaymath}
\partial^\mu \equiv \frac{\partial}{\partial x_\mu} = \left(-\nabla,
\frac{1}{c}\frac{\partial}{\partial t}\right),
\end{displaymath}">|; 

$key = q/Deltax>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2766.png"
 ALT="$\Delta x&gt;0$">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}=frac{e^2,r}{16pi^2,epsilon_0,c^3}frac{[{{bf{r}times({{bf{r}_utimesdot{{bf{u})]^2}{s^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3342.png"
 ALT="\begin{displaymath}
\frac{dP(t')}{d{\mit\Omega}} = \frac{e^2  r}{16\pi^2 
\eps...
...^3} \frac{[{\bf r}\times({\bf r}_u\times\dot{\bf u})]^2}{s^5}.
\end{displaymath}">|; 

$key = q/varphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2226.png"
 ALT="$\varphi$">|; 

$key = q/{displaymath}A_{{rm{eff}=0.13,lambda^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2261.png"
 ALT="\begin{displaymath}
A_{\rm eff} = 0.13 \lambda^2.
\end{displaymath}">|; 

$key = q/{displaymath}g_{mu'nu'},p_{sigma}^{mu'}p_{numu}^{nu'}+g_{mu'nu'},p_{mu}^{mu'}p_{nusigma}^{nu'}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2922.png"
 ALT="\begin{displaymath}
g_{\mu'\nu'} p_{\sigma}^{\mu'}
p_{\nu\mu}^{\nu'} + g_{\mu'\nu'} 
p_{\mu}^{\mu'}p_{\nu\sigma}^{\nu'} = 0,
\end{displaymath}">|; 

$key = q/oint{{bf{A}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="$\oint {\bf A}\cdot d{\bf S}$">|; 

$key = q/g_{munu},dx^mu,dx^nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2915.png"
 ALT="$g_{\mu\nu}  dx^\mu  dx^\nu$">|; 

$key = q/{{bf{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="${\bf I}$">|; 

$key = q/{displaymath}frac{dgamma}{dt}=gamma^3,frac{{{bf{u}!cdotdot{{bf{u}}{c^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3319.png"
 ALT="\begin{displaymath}
\frac{d\gamma}{dt} = \gamma^3 \frac{{\bf u}\!\cdot\dot{\bf u}}{c^2}.
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot(phi_3,{{bf{E}_3)equivphi_3,nablacdot{{bf{E}_3+{{bf{E}_3cdotnablaphi_3.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1444.png"
 ALT="\begin{displaymath}
\nabla\cdot(\phi_3 {\bf E}_3) \equiv \phi_3 \nabla \cdot{\bf E}_3 + {\bf E}_3\cdot
\nabla\phi_3.
\end{displaymath}">|; 

$key = q/{mitdiv},,{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="${\mit div}  {\bf v}$">|; 

$key = q/{displaymath}dx^2+dy^2+dz^2-c^2,dt^2=d{x'}^2+d{y'}^2+d{z'}^2-c^2,d{t'}^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="434" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2853.png"
 ALT="\begin{displaymath}
dx^2 + dy^2 + dz^2 - c^2 dt^2 = d{x'}^2 + d{y'}^2+d{z'}^2 -c^2 d{t'}^2.
\end{displaymath}">|; 

$key = q/d^3{{bf{r}'=dl_1,dA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1876.png"
 ALT="$d^3{\bf r}' = dl_1  dA$">|; 

$key = q/oint_S{{bf{B}!cdot!d{{bf{S}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="$\oint_S {\bf B}\!\cdot \!d{\bf S} \neq 0$">|; 

$key = q/A_mu,B^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3303.png"
 ALT="$A_\mu  B^\mu$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{1}{4pi,epsilon_0}intfrac{rho({{bf{r}',t_r)}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{1}{4\pi \epsilon_0} \int \frac{ \rho({\bf r}', t_r)}{\vert{\bf r} - {\bf r}'\vert} 
d^3{\bf r}',
\end{displaymath}">|; 

$key = q/lambda=epsilon_0mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$\lambda = \epsilon_0\mu_0$">|; 

$key = q/A';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1705.png"
 ALT="$A'$">|; 

$key = q/{displaymath}delta(x)=lim_{epsilonrightarrow0}g(x,epsilon).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="\begin{displaymath}
\delta(x) = \lim_{\epsilon\rightarrow 0} g(x,\epsilon).
\end{displaymath}">|; 

$key = q/{displaymath}M_{21}=M_{12}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1880.png"
 ALT="\begin{displaymath}
M_{21} = M_{12}.
\end{displaymath}">|; 

$key = q/i=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1423.png"
 ALT="$i=1$">|; 

$key = q/{displaymath}(E_i-E_r),frac{costheta_i}{v_1}=E_t,frac{costheta_t}{v_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2538.png"
 ALT="\begin{displaymath}
(E_i -E_r) \frac{\cos\theta_i}{v_1} = E_t \frac{\cos\theta_t}{v_2}.
\end{displaymath}">|; 

$key = q/displaystylefrac{partialA_x}{partialx}+frac{partialA_y}{partialy}+frac{partialA_},{{rm{i},k_z),{{rm{e}^{,{{rm{i},({{bf{k}cdot{{bf{r}-omegat)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="$\displaystyle \frac{\partial A_x}{\partial x}+
\frac{\partial A_y}{\partial y}+...
...A_{0z}  {\rm i}  k_z)
 {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r} - \omega t)}$">|; 

$key = q/omegaggomega_p,{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2377.png"
 ALT="$\omega \gg \omega_p, {\mit \Omega}$">|; 

$key = q/{displaymath}I(t)=frac{V}{R}left[1-exp(-R,tslashL),right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1901.png"
 ALT="\begin{displaymath}
I(t) = \frac{V}{R} \left[1-\exp(-R t/L) \right].
\end{displaymath}">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2952.png"
 ALT="$e$">|; 

$key = q/x^{i'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2780.png"
 ALT="$x^{i'}$">|; 

$key = q/{{bf{B}=nablatimes{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1977.png"
 ALT="${\bf B} = \nabla\times{\bf A}$">|; 

$key = q/jneqi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$j\neq i$">|; 

$key = q/{displaymath}{{bf{a},{{rm{x},{{bf{b}=(a_x,b_x,,a_y,b_y,,a_z,b_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="\begin{displaymath}
{\bf a}  {\rm x}  {\bf b} = (a_x  b_x,  a_y  b_y,  a_z  b_z).
\end{displaymath}">|; 

$key = q/displaystyleoint_C{{bf{B}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$\displaystyle \oint_C {\bf B} \cdot d{\bf l}$">|; 

$key = q/G({{bf{r},{{bf{r}';t,t');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="$G({\bf r}, {\bf r}'; t, t')$">|; 

$key = q/{displaymath}x^2+y^2=c^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1585.png"
 ALT="\begin{displaymath}
x^2+y^2 = c^2,
\end{displaymath}">|; 

$key = q/{displaymath}dx'=gammaleft(1+frac{v}{c},costhetaright)dx,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2995.png"
 ALT="\begin{displaymath}
dx' = \gamma\left(1+\frac{v}{c}  \cos\theta\right) dx,
\end{displaymath}">|; 

$key = q/U=(epsilon_0slash2),E^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="$U = (\epsilon_0/2) E^{2}$">|; 

$key = q/K=pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2687.png"
 ALT="$K=\pm 1$">|; 

$key = q/displaystylefrac{sigma}{epsilon_0}mbox{hspace{2cm}between},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle \frac{\sigma }{\epsilon_0}\mbox{\hspace{2cm} between},$">|; 

$key = q/displaystyle0mbox{hspace{2.5cm}below},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="$\displaystyle 0 \mbox{\hspace{2.5cm} below},$">|; 

$key = q/{displaymath}alpha=frac{{{bf{r}cdot{{bf{b}times{{bf{c}}{{{bf{a}cdot{{bf{b}times{{bf{c}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="\begin{displaymath}
\alpha = \frac{{\bf r}\cdot{\bf b}\times{\bf c}}{{\bf a}\cdot{\bf b}\times{\bf c}}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3}=-nabla!left(frac{1}{|{{bf{r}-{{bf{r'}|}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="\begin{displaymath}
\frac{{\bf r}- {\bf r}' }
{\vert{\bf r} - {\bf r}'\vert^3} = -\nabla\!\left(\frac{1}{\vert{\bf r} - {\bf r'}\vert}\right),
\end{displaymath}">|; 

$key = q/{displaymath}rho=gamma(u),rho_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2959.png"
 ALT="\begin{displaymath}
\rho = \gamma(u)  \rho_0.
\end{displaymath}">|; 

$key = q/{{bf{B}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="${\bf B}'$">|; 

$key = q/{displaymath}sigma_b=-epsilon_0left(left.frac{partialphi}{partialr}right|_{r=a+}=3,epsilon_0,frac{epsilon-1}{epsilon+2}costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img1747.png"
 ALT="\begin{displaymath}
\sigma_b = -\epsilon_0\left(\left.\frac{\partial\phi}{\parti...
...ht) =
3 \epsilon_0 \frac{\epsilon-1}{\epsilon+2}\cos\theta.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{rho({{bf{r'})}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int \frac{\rho({\bf r'})}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r'}$">|; 

$key = q/{displaymath}int_SG_{ij},dS_jequivint_Vfrac{partialG_{ij}}{partialx_j},dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2172.png"
 ALT="\begin{displaymath}
\int_S G_{ij} dS_j \equiv \int_V \frac {\partial G_{ij}}{\partial x_j} dV,
\end{displaymath}">|; 

$key = q/A^mu=({{bf{A},A^0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2911.png"
 ALT="$A^\mu= ({\bf A}, A^0)$">|; 

$key = q/rho_b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1673.png"
 ALT="$\rho_b$">|; 

$key = q/vslashcrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2718.png"
 ALT="$v/c\rightarrow 0$">|; 

$key = q/dVslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2987.png"
 ALT="$dV/r$">|; 

$key = q/{{bf{E}=E_r(r),hat{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="${\bf E} = E_r(r) \hat
{\bf r}$">|; 

$key = q/1slashsqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2031.png"
 ALT="$1/\sqrt{2}$">|; 

$key = q/{displaymath}p_{musigma}^{mu'}=frac{partialp_mu^{mu'}}{partialx^sigma}=frac{part{partialx^{mu}partialx^sigma}=p_{sigmamu}^{mu'},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2920.png"
 ALT="\begin{displaymath}
p_{\mu\sigma}^{\mu'} = \frac{\partial p_\mu^{\mu'} }{\partia...
...mu'}}{\partial x^{\mu}\partial
x^\sigma}=p_{\sigma\mu}^{\mu'},
\end{displaymath}">|; 

$key = q/displaystylemu_0,{{bf{j}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$\displaystyle \mu_0  {\bf j}.$">|; 

$key = q/displaystyleB_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1827.png"
 ALT="$\displaystyle B_1$">|; 

$key = q/{displaymath}f=frac{q^2}{4pi,epsilon_0,(b-c)^2}=frac{q,q'}{4pi},frac{a,b}{(b^2-a^2)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1533.png"
 ALT="\begin{displaymath}
f = \frac{q^2}{4\pi \epsilon_0 (b-c)^2} = \frac{q q'}{4\pi} \frac{a b}{(b^2-a^2)^2}.
\end{displaymath}">|; 

$key = q/displaystyleA_z({{bf{r})=frac{mu_0}{4pi}intfrac{j_z({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="$\displaystyle A_z({\bf r}) = \frac{\mu_0}{4\pi} \int \frac{j_z({\bf r}')}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r}'.$">|; 

$key = q/displaystyleCsin(k,y)+Dcos(k,y),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1619.png"
 ALT="$\displaystyle C \sin (k y) + D \cos (k y),$">|; 

$key = q/{displaymath}R=eta,frac{l}{A}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="\begin{displaymath}
R = \eta  \frac{l}{A}.
\end{displaymath}">|; 

$key = q/trightarrow-t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="$t\rightarrow -t$">|; 

$key = q/nablaU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$\nabla U$">|; 

$key = q/{displaymath}mu_0nablacdot{{bf{j}+frac{lambda}{epsilon_0}frac{partialrho}{partialt}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="\begin{displaymath}
\mu_0 \nabla\cdot{\bf j} + \frac{\lambda}{\epsilon_0} \frac{\partial\rho}{\partial t}
=0.
\end{displaymath}">|; 

$key = q/{{bf{j}({{bf{r}',t-|{{bf{r}-{{bf{r}'|slashc),d^3{{bf{r}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2207.png"
 ALT="${\bf j}({\bf r}', t- \vert{\bf r} - {\bf r}'\vert/c)
 d^3{\bf r}'$">|; 

$key = q/t^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2712.png"
 ALT="$t^2$">|; 

$key = q/{displaymath}U=frac{1}{2},{{bf{H}!cdot{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1859.png"
 ALT="\begin{displaymath}
U=\frac{1}{2}  {\bf H}\!\cdot{\bf B}.
\end{displaymath}">|; 

$key = q/partial^2Tslashpartialy^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\partial^2 T/\partial y^2$">|; 

$key = q/U^mu=({{bf{0},c);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2948.png"
 ALT="$U^\mu=({\bf0}, c)$">|; 

$key = q/displaystyle{{bf{E}(z<0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1513.png"
 ALT="$\displaystyle {\bf E}(z&lt;0)$">|; 

$key = q/{displaymath}nabla!cdot!{{bf{B}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1807.png"
 ALT="\begin{displaymath}
\nabla\!\cdot\!{\bf B} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}-{{bf{E}cdot{{bf{j}=nabla!cdot!left(frac{{{bf{E}times{{bf{B}}{mu_0}al}{partialt}!left(frac{epsilon_0,E^2}{2}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="410" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2120.png"
 ALT="\begin{displaymath}
- {\bf E} \cdot {\bf j} = \nabla \!\cdot\!
\left(\frac{{\bf ...
...partial}{\partial t}\!\left(\frac{\epsilon_0  E^2}{2}\right).
\end{displaymath}">|; 

$key = q/|r|rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="$\vert r\vert\rightarrow 0$">|; 

$key = q/{displaymath}int_P^Qleft(y^3,dx+3,x,y^2,dyright)=left[x,y^3right]_P^Q{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="\begin{displaymath}
\int_P^Q \left(y^3 dx + 3 x y^2 dy\right) = \left[x y^3\right]_P^Q
\end{displaymath}">|; 

$key = q/{displaymath}deltambox{{boldmath{{theta{}=deltatheta_x,{{bf{e}_x+deltatheta_y,{{bf{e}_y+deltatheta_z,{{bf{e}_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="\begin{displaymath}
\delta\mbox{\boldmath$\theta$} = \delta\theta_x  {\bf e}_x + \delta\theta_y  {\bf e}_y +
\delta\theta_z  {\bf e}_z.
\end{displaymath}">|; 

$key = q/dtau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$d\tau$">|; 

$key = q/V_0,cos(omega,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2057.png"
 ALT="$V_0  \cos(\omega  t)$">|; 

$key = q/theta_0rightarrowpm1slashgamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3378.png"
 ALT="$\theta_0 \rightarrow \pm 1/\gamma$">|; 

$key = q/{displaymath}{mitPhi}^mu=frac{1}{4pi,epsilon_0,c}intfrac{[J^mu]}{r},dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3124.png"
 ALT="\begin{displaymath}
{\mit\Phi}^\mu = \frac{1}{4\pi \epsilon_0 c}\int
\frac{[J^\mu]}{r} dV,
\end{displaymath}">|; 

$key = q/d{{bf{l}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1866.png"
 ALT="$d{\bf l}_1$">|; 

$key = q/10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="$10^4$">|; 

$key = q/{displaymath}int_0^1left(frac{y}{3}-y^2+y^3-frac{y^4}{3}right)dy=frac{1}{60}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="\begin{displaymath}
\int_0^1 \left(\frac{y}{3} - y^2 + y^3- \frac{y^4}{3}\right)dy = \frac{1}{60}.
\end{displaymath}">|; 

$key = q/{mitdiv},{{bf{v}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="${\mit div} {\bf v}=0$">|; 

$key = q/x=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="$x=x_0$">|; 

$key = q/{displaymath}{{bf{B}=frac{mu_0,I}{2pi}left(frac{-y}{r^2},,frac{x}{r^2},,0right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="\begin{displaymath}
{\bf B} = \frac{\mu_0  I}{2\pi}\left(\frac{-y}{r^2},  \frac{x}{r^2},  0 \right)
\end{displaymath}">|; 

$key = q/-pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2035.png"
 ALT="$-\pi/2$">|; 

$key = q/{displaymath}P=frac{1}{2},{{rm{Re}(Z),|I|^2=frac{1}{2}frac{{{rm{Re}(Z),|V|^2}{|Z|^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2027.png"
 ALT="\begin{displaymath}
P = \frac{1}{2}  {\rm Re}(Z)  \vert I\vert^2 = \frac{1}{2} \frac{{\rm Re}(Z) \vert V\vert^2}{\vert Z\vert^2}.
\end{displaymath}">|; 

$key = q/(1slashc^2)(partial^2Gslashpartialt^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="$(1/c^2)(\partial^2 G/\partial t^2)$">|; 

$key = q/OQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$OQ$">|; 

$key = q/{displaymath}P=lim_{deltatrightarrow0}frac{deltaW}{deltat}={{bf{f}cdot{{bf{v},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="\begin{displaymath}
P = \lim_{\delta t\rightarrow 0} \frac{\delta W}{\delta t} = {\bf f}\cdot
{\bf v},
\end{displaymath}">|; 

$key = q/displaystylek_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2614.png"
 ALT="$\displaystyle k_y$">|; 

$key = q/c=omegaslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$c = \omega/k$">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1884.png"
 ALT="$L$">|; 

$key = q/displaystylefrac{partial}{partialx}!left(frac{partialT}{partialx}right)+frac{par)+frac{partial}{partialz}!left(frac{partialT}{partialz}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$\displaystyle \frac{\partial}{\partial x}\!\left(\frac{\partial T}{\partial x}\...
...right)+
\frac{\partial}{\partial z}\!\left(\frac{\partial T}{\partial z}\right)$">|; 

$key = q/lambda=2pi,cslashomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2038.png"
 ALT="$\lambda = 2\pi  c/\omega$">|; 

$key = q/displaystyleint_P^Qx,y,dl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle \int_P^Q x y dl$">|; 

$key = q/ds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2860.png"
 ALT="$ds$">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle {\bf a} \cdot {\bf b}$">|; 

$key = q/{displaymath}nabla^2phi=-frac{rho}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="\begin{displaymath}
\nabla^2\phi = -\frac{\rho}{\epsilon_0},
\end{displaymath}">|; 

$key = q/sin(n,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1627.png"
 ALT="$\sin (n y)$">|; 

$key = q/{displaymath}int_P^Qleft[f(x,y),dx+g(x,y),dyright].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="\begin{displaymath}
\int_P^Q \left[ f(x,y) dx + g(x,y) dy\right].
\end{displaymath}">|; 

$key = q/{displaymath}V_i=-frac{d{mitPhi}_i}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1980.png"
 ALT="\begin{displaymath}
V_i = - \frac{d {\mit\Phi}_i}{dt}.
\end{displaymath}">|; 

$key = q/displaystyleU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1572.png"
 ALT="$\displaystyle U$">|; 

$key = q/int_V{{bf{E}cdot{{bf{j},dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2113.png"
 ALT="$\int_V {\bf E}\cdot{\bf j} dV$">|; 

$key = q/n=n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1633.png"
 ALT="$n=n'$">|; 

$key = q/{displaymath}c=frac{1}{sqrt{epsilon_0,mu_0}}=2.99729times10^8,,mbox{meterspersecond},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2650.png"
 ALT="\begin{displaymath}
c = \frac{1}{\sqrt{\epsilon_0  \mu_0}}=2.99729\times 10^8  \mbox{meters per second},
\end{displaymath}">|; 

$key = q/{displaymath}dx'^2+dy'^2+dz'^2-c^2,dt'^2=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2667.png"
 ALT="\begin{displaymath}
dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2 = 0
\end{displaymath}">|; 

$key = q/displaystyle{{bf{a}cdot{{bf{b}+{{bf{a}cdot{{bf{c}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle {\bf a} \cdot {\bf b} + {\bf a}\cdot {\bf c}.$">|; 

$key = q/A^mu=({{bf{a},0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2949.png"
 ALT="$A^\mu = ({\bf a}, 0)$">|; 

$key = q/dS_mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3287.png"
 ALT="$dS_\mu$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig24.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig24.eps}}
\end{figure}">|; 

$key = q/displaystyleB_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3096.png"
 ALT="$\displaystyle B_\parallel,$">|; 

$key = q/{displaymath}W=frac{1}{4pi,epsilon_0}left(frac{q_2,q_1}{|{{bf{r}_2-{{bf{r}_1|}+f_1|}+frac{q_3,q_2}{|{{bf{r}_3-{{bf{r}_2|}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="\begin{displaymath}
W = \frac{1}{4\pi  \epsilon_0}\left( \frac{q_2  q_1}{\vert...
...t}
+ \frac{q_3  q_2}{\vert{\bf r}_3 - {\bf r}_2\vert}\right).
\end{displaymath}">|; 

$key = q/+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3012.png"
 ALT="$+1$">|; 

$key = q/{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="${\bf j}$">|; 

$key = q/eslash(4pi,epsilon_0,{r'}^3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3128.png"
 ALT="$e/(4\pi \epsilon_0 {r'}^3)$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{BH.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img1800.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{BH.eps}}
\end{figure}">|; 

$key = q/{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="${\bf A}$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig30.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="225" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig30.eps}}
\end{figure}">|; 

$key = q/I_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1946.png"
 ALT="$I_T$">|; 

$key = q/displaystyle-nablaphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2639.png"
 ALT="$\displaystyle - \nabla\phi,$">|; 

$key = q/{displaymath}frac{dE}{dt}=frac{d(m,c^2)}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img3160.png"
 ALT="\begin{displaymath}
\frac{dE}{dt} = \frac{d (m c^2)}{dt},
\end{displaymath}">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\theta$">|; 

$key = q/{displaymath}{{bf{S}={{bf{a}times{{bf{b},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="\begin{displaymath}
{\bf S} = {\bf a}\times {\bf b},
\end{displaymath}">|; 

$key = q/delta_{ij}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2194.png"
 ALT="$\delta_{ij}=0$">|; 

$key = q/{displaymath}partial_muF_{nusigma}+partial_nuF_{sigmamu}+partial_sigmaF_{munu}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3189.png"
 ALT="\begin{displaymath}
\partial_\mu F_{\nu\sigma} + \partial_\nu F_{\sigma\mu} +
\partial_\sigma F_{\mu\nu} = 0.
\end{displaymath}">|; 

$key = q/delta(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="$\delta(x)$">|; 

$key = q/IslashA=j_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="$I/A = j_z$">|; 

$key = q/{figure}{epsfysize{=1.75in{centerline{epsffile{fig5.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="201" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="\begin{figure}
\epsfysize =1.75in
\centerline{\epsffile{fig5.eps}}
\end{figure}">|; 

$key = q/displaystylenabla!cdot!{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2311.png"
 ALT="$\displaystyle \nabla\!\cdot\!{\bf E}$">|; 

$key = q/cosphi=costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3372.png"
 ALT="$\cos\phi=\cos\theta$">|; 

$key = q/mu_0,{{bf{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1804.png"
 ALT="$\mu_0 {\bf H}$">|; 

$key = q/Q^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2903.png"
 ALT="$Q^\mu$">|; 

$key = q/{displaymath}beta=frac{v_1}{v_2}=frac{n_2}{n_1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img2540.png"
 ALT="\begin{displaymath}
\beta = \frac{v_1}{v_2}= \frac{n_2}{n_1}.
\end{displaymath}">|; 

$key = q/{displaymath}n=sqrt{epsilon}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2317.png"
 ALT="\begin{displaymath}
n = \sqrt{\epsilon}
\end{displaymath}">|; 

$key = q/phi(k)=k,x-omega(k),t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2336.png"
 ALT="$\phi(k) = k x-\omega(k) t$">|; 

$key = q/{displaymath}nablatimes({{bf{A}times{{bf{B})={{bf{A},(nablacdot{{bf{B})-{{bf{B},bf{B}cdotnabla){{bf{A}-({{bf{A}cdotnabla){{bf{B}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="\begin{displaymath}
\nabla\times({\bf A}\times{\bf B}) = {\bf A} (\nabla\cdot {...
... A}) +({\bf B}\cdot\nabla){\bf A}- ({\bf A}\cdot\nabla){\bf B}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{W}({{bf{r})=frac{1}{4pi}intfrac{{{bf{C}({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="\begin{displaymath}
{\bf W} ({\bf r})= \frac{1}{4\pi } \int\frac{{\bf C}({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'}.
\end{displaymath}">|; 

$key = q/displaystyle-(dx^1)^2-(dx^2)^2-(dx^3)^2+(dx^4)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2865.png"
 ALT="$\displaystyle -(dx^1)^2 -(dx^2)^2 -(dx^3)^2 + (dx^4)^2$">|; 

$key = q/sigma_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2292.png"
 ALT="$\sigma_T$">|; 

$key = q/10^{-10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="$10^{-10}$">|; 

$key = q/B=Eslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2127.png"
 ALT="$B=E/c$">|; 

$key = q/{displaymath}int_Vpartial_muT^mu,d^4x=oint_ST^mu,dS_mu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img3286.png"
 ALT="\begin{displaymath}
\int_V \partial_\mu T^\mu  d^4 x = \oint_S T^\mu dS_\mu,
\end{displaymath}">|; 

$key = q/d{{bf{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3310.png"
 ALT="$d{\bf p}$">|; 

$key = q/displaystyle-G^{4i}=-c,B^i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3065.png"
 ALT="$\displaystyle - G^{4i} = - c B^i,$">|; 

$key = q/E_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1744.png"
 ALT="$E_1$">|; 

$key = q/displaystyle{{bf{A}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3104.png"
 ALT="$\displaystyle {\bf A}'$">|; 

$key = q/Urightarrowx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1582.png"
 ALT="$U\rightarrow x$">|; 

$key = q/{{bf{a}={{bf{a}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="${\bf a} = {\bf a} (t)$">|; 

$key = q/displaystylemu_0int_{S'}{{bf{j}cdotd{{bf{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="$\displaystyle \mu_0 \int_{S'} {\bf j} \cdot d{\bf S}.$">|; 

$key = q/displaystyle0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle 0.$">|; 

$key = q/S(x,y,z,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2651.png"
 ALT="$S(x,y,z,t)$">|; 

$key = q/{displaymath}costheta=frac{{{bf{u}!cdot!{{bf{r}}{u,r}=sinalpha,cosphi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3365.png"
 ALT="\begin{displaymath}
\cos\theta = \frac{{\bf u}\!\cdot\!{\bf r}}{u  r} = \sin\alpha \cos\phi.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{curl},({{bf{grad},phi)equiv{{bf{0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="\begin{displaymath}
{\bf curl} ({\bf grad} \phi)\equiv {\bf0}.
\end{displaymath}">|; 

$key = q/(1slashsqrt{2},0,1slashsqrt{2},1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2679.png"
 ALT="$(1/\sqrt{2}, 0, 1/\sqrt{2}, 1)$">|; 

$key = q/{displaymath}c=frac{1}{sqrt{epsilon_0mu_0}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="\begin{displaymath}
c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}.
\end{displaymath}">|; 

$key = q/A_{ijcdotsk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2789.png"
 ALT="$A_{ij\cdots k}$">|; 

$key = q/displaystyleE_{{rm{lower};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="$\displaystyle E_{\rm lower }$">|; 

$key = q/{displaymath}frac{1}{r}frac{partial}{partialr}left(r,frac{partialphi}{partialr}right)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2645.png"
 ALT="\begin{displaymath}
\frac{1}{r}\frac{\partial}{\partial r}\left( r \frac{\partial \phi}{\partial r}\right) = 0,
\end{displaymath}">|; 

$key = q/{displaymath}F^{musigma},partial_muF_{nusigma}=-frac{1}{2},F^{musigma},partial_n}=frac{1}{4},partial_nu(F^{musigma}F_{musigma}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3193.png"
 ALT="\begin{displaymath}
F^{\mu\sigma}  \partial_\mu F_{\nu\sigma} = - \frac{1}{2} ...
...u} = \frac{1}{4}  \partial_\nu (F^{\mu\sigma}
F_{\mu\sigma}).
\end{displaymath}">|; 

$key = q/E_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2370.png"
 ALT="$E_+$">|; 

$key = q/{displaymath}{{bf{A}({{bf{r},t)=frac{mu_0,{{bf{j}({{bf{r'},t')}{4pi}frac{delta(t-|{{bf{r}-{{bf{r'}|slashc)}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="\begin{displaymath}
{\bf A}({\bf r}, t) = \frac{\mu_0 {\bf j}({\bf r'}, t')}{4\...
...vert{\bf r} - {\bf r'}\vert/c)}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{P}{m_0,c^2}=frac{2}{3}left(frac{e,B}{m_0}right)^2frac{r_0}{c},(beta,gamma)^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3389.png"
 ALT="\begin{displaymath}
\frac{P}{m_0  c^2} =\frac{2}{3} \left(\frac{e B}{m_0}\right)^2
\frac{r_0}{c}  (\beta \gamma)^2,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="\begin{displaymath}
{\bf f} = q {\bf E},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig35.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig35.eps}}
\end{figure}">|; 

$key = q/R=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2085.png"
 ALT="$R=0$">|; 

$key = q/{displaymath}W=frac{Q^2}{8pi,epsilon_0,a}left(frac{1}{5}+1right)=frac{3}{5}frac{Q^2}{4pi,epsilon_0,a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="\begin{displaymath}
W = \frac{Q^2}{8\pi \epsilon_0  a} \left( \frac{1}{5} + 1\right)=
\frac{3}{5} \frac{Q^2}{4\pi \epsilon_0  a}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{p}=frac{e^2}{m_e,(omega_0^{,2}-omega^2)},{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2320.png"
 ALT="\begin{displaymath}
{\bf p} = \frac{e^2}{m_e (\omega_0^{ 2}-\omega^2)} {\bf E},
\end{displaymath}">|; 

$key = q/V_2(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1937.png"
 ALT="$V_2(t)$">|; 

$key = q/{displaymath}frac{f_{{rm{magnetic}}{f_{{rm{electric}}simfrac{v,B_0}{E_0}simfrac{v}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="\begin{displaymath}
\frac{f_{\rm magnetic}}{f_{\rm electric}} \sim \frac{v B_0}{E_0} \sim
\frac{v}{c}.
\end{displaymath}">|; 

$key = q/R=Z_{{rm{in};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2065.png"
 ALT="$R= Z_{\rm in}$">|; 

$key = q/Rllsqrt{LslashC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2033.png"
 ALT="$R \ll \sqrt{L/C}$">|; 

$key = q/stackrel{displaystylerightarrow}{PR},=,stackrel{displaystylerightarrow}{PQ}+stackrel{displaystylerightarrow}{QR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{PR}
 = 
\stackrel{\displaystyle \rightarrow}{PQ}+ \stackrel{\displaystyle \rightarrow}{QR}$">|; 

$key = q/{displaymath}-partial_i,(c,B^i)=partial_iG^{i4}+partial_4G^{44}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3084.png"
 ALT="\begin{displaymath}
-\partial_i (c B^i) = \partial_i G^{i4} +\partial_4 G^{44} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}dx'^2+dy'^2+dz'^2-c^2,dt'^2=K,(dx^2+dy^2+dz^2-c^2,dt^2),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2674.png"
 ALT="\begin{displaymath}
dx'^2 + dy'^2 + dz'^2 -c^2  dt'^2 = K (dx^2 + dy^2 + dz^2 -c^2  dt^2),
\end{displaymath}">|; 

$key = q/{{bf{e}_zequiv(0,0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="${\bf e}_z \equiv
(0,0,1)$">|; 

$key = q/f({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="$f({\bf r})$">|; 

$key = q/r^i=x^i-{x^i}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3231.png"
 ALT="$r^i = x^i - {x^i}'$">|; 

$key = q/displaystyleP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2017.png"
 ALT="$\displaystyle P$">|; 

$key = q/10^{-29},{{rm{m^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2288.png"
 ALT="$10^{-29} {\rm m^2}$">|; 

$key = q/displaystylefrac{partialB_x}{partialz}-frac{partialB_z}{partialx}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="$\displaystyle \frac{\partial B_x}{\partial z} - \frac{\partial B_z}
{\partial x} = 0,$">|; 

$key = q/[rho({{bf{r},t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$[\rho({\bf r}, t)]$">|; 

$key = q/oint{{bf{A}cdotd{{bf{l}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$\oint {\bf A}\cdot d{\bf l}=0$">|; 

$key = q/{{bf{b}times{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="${\bf b}\times {\bf c}$">|; 

$key = q/{calV},U(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1577.png"
 ALT="${\cal V}  U(x, y)$">|; 

$key = q/f(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$f(x)$">|; 

$key = q/{displaymath}frac{dP}{d{mitOmega}}=frac{omega^4,p_0^{,2}}{32pi^2,epsilon_0,c^3},sin^2theta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2268.png"
 ALT="\begin{displaymath}
\frac{dP}{d{\mit\Omega}} = \frac{\omega^4 p_0^{ 2}}{32\pi^2 \epsilon_0 c^3} \sin^2\theta.
\end{displaymath}">|; 

$key = q/{displaymath}B_x={{rm{i},left(-frac{omega}{c^2}frac{partialE_z}{partialy}+k,fraclx}right)left(frac{omega^2}{c^2}-k^2right)^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2592.png"
 ALT="\begin{displaymath}
B_x = {\rm i} \left(-\frac{\omega}{c^2}\frac{\partial E_z}{...
...{\partial x}\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}u({{bf{r})=intG({{bf{r},,{{bf{r}'),v({{bf{r}'),d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="\begin{displaymath}
u({\bf r}) = \int G({\bf r},  {\bf r}')  v({\bf r}') d^3 {\bf r}'.
\end{displaymath}">|; 

$key = q/{displaymath}deltaE({{rm{MeV})=8.85times10^{-2},frac{[E({{rm{GeV})]^4}{rho({{rm{meters})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="292" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3333.png"
 ALT="\begin{displaymath}
\delta E ({\rm MeV}) = 8.85\times 10^{-2}  \frac{[E({\rm GeV})]^4}{\rho
({\rm meters})}.
\end{displaymath}">|; 

$key = q/{displaymath}{calJ}=frac{partial(x^{1'},x^{2'},x^{3'},x^{4'})}{partial(x^{1},x^{2},x^{3},x^{4})}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2938.png"
 ALT="\begin{displaymath}
{\cal J} = \frac{\partial(x^{1'}, x^{2'}, x^{3'}, x^{4'})}
{\partial (x^{1}, x^{2}, x^{3}, x^{4})}
\end{displaymath}">|; 

$key = q/{displaymath}{calF}^mu=gammaleft({{bf{f},c,frac{dm}{dt}right)=gammaleft({{bf{f},frac{{{bf{f}!cdot!{{bf{u}}{c}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3168.png"
 ALT="\begin{displaymath}
{\cal F}^\mu = \gamma\left({\bf f}, c  \frac{dm}{dt}\right)...
...amma \left( {\bf f}, \frac{{\bf f}\!\cdot\!{\bf u}}{c}\right),
\end{displaymath}">|; 

$key = q/S';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="$S'$">|; 

$key = q/displaystyleleft(frac{alpha-beta}{alpha+beta}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2561.png"
 ALT="$\displaystyle \left(\frac{\alpha-\beta}{\alpha+\beta}\right)^2,$">|; 

$key = q/{displaymath}phi(0,y)=phi_0(y){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1602.png"
 ALT="\begin{displaymath}
\phi(0, y) = \phi_0(y)
\end{displaymath}">|; 

$key = q/S_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1449.png"
 ALT="$S_i$">|; 

$key = q/displaystyle{mitdiv},({{bf{grad},T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$\displaystyle {\mit div} ({\bf grad} T)$">|; 

$key = q/r<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="$r&lt;a$">|; 

$key = q/{{bf{k}cdot{{bf{r}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="${\bf k}\cdot{\bf r} = 0$">|; 

$key = q/{displaymath}E_z=E_0,{{rm{e}^{,{{rm{i},({{rm{i},|k|,x-omega,t)}=E_0,{{rm{e}^{-|k|,x},{{rm{e}^{-{{rm{i},omega,t}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img2349.png"
 ALT="\begin{displaymath}
E_z = E_0 {\rm e}^{ {\rm i} ({\rm i} \vert k\vert x-\om...
..._0 {\rm e}^{-\vert k\vert x} {\rm e}^{-{\rm i} \omega t}.
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2u_1=v_1,mbox{hspace{1cm}}nabla^2u_2=v_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="\begin{displaymath}
\nabla^2 u_1 = v_1, \mbox{\hspace{1cm}} \nabla^2 u_2=v_2,
\end{displaymath}">|; 

$key = q/displaystyle+frac{sigma}{2,epsilon_0}mbox{hspace{2cm}above},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="$\displaystyle +\frac{\sigma }{2 \epsilon_0} \mbox{\hspace{2cm} above},$">|; 

$key = q/f^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3188.png"
 ALT="$f^\mu$">|; 

$key = q/dot{u}=a,omega_0^{~2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3363.png"
 ALT="$\dot{u}=a \omega_0^{&nbsp;2}$">|; 

$key = q/oint{{bf{curl},{{bf{A}cdotd{{bf{S}=int{mitdiv},({{bf{curl},{{bf{A}),dV=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$\oint{\bf curl} {\bf A}\cdot d{\bf S} = \int {\mit div} ({\bf curl} {\bf A})  dV
=0$">|; 

$key = q/displaystyle(nablatimes{{bf{B})_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$\displaystyle (\nabla\times{\bf B})_y$">|; 

$key = q/p_0=e^2,E_0slash(m_e,omega^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2276.png"
 ALT="$p_0 = e^2 E_0/(m_e  \omega^2)$">|; 

$key = q/omega<omega_{mn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2624.png"
 ALT="$\omega &lt; \omega_{mn}$">|; 

$key = q/{displaymath}E=m,c^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img3161.png"
 ALT="\begin{displaymath}
E = m  c^2.
\end{displaymath}">|; 

$key = q/i,j,k,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2875.png"
 ALT="$i,j,k,$">|; 

$key = q/{displaymath}G_{ij}=epsilon_0,(E^2,delta_{ij}slash2-E_i,E_j)+(B^2,delta_{ij}slash2-B_i,B_j)slashmu_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2195.png"
 ALT="\begin{displaymath}
G_{ij} = \epsilon_0 (E^2 \delta_{ij}/2-E_i E_j) + (B^2 \delta_{ij}/2-B_i B_j)/ \mu_0.
\end{displaymath}">|; 

$key = q/{displaymath}frac{dP(t')}{d{mitOmega}}simeqfrac{2,e^2,dot{u}^2}{pi^2,epsilon_0c^a^8frac{(gamma,theta)^2}{[1+(gamma,theta)^2]^5}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="259" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3351.png"
 ALT="\begin{displaymath}
\frac{dP(t')}{d{\mit\Omega}} \simeq \frac{2  e^2 \dot{u}^2...
...\gamma^8 \frac{(\gamma \theta)^2}{[1+ (\gamma \theta)^2]^5}.
\end{displaymath}">|; 

$key = q/2.3times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1787.png"
 ALT="$2.3\times 10^{-5}$">|; 

$key = q/{displaymath}oint_S{{bf{A}cdotd{{bf{S}=int_V{mitdiv},{{bf{A},,dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="\begin{displaymath}
\oint_S {\bf A}\cdot d{\bf S} = \int_V {\mit div}  {\bf A}  dV.
\end{displaymath}">|; 

$key = q/E_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1731.png"
 ALT="$E_\parallel$">|; 

$key = q/{displaymath}deltaE=frac{2pi,rho}{u}P=frac{e^2}{3,epsilon_0,c^3}frac{gamma^4,u^3}{rho}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3332.png"
 ALT="\begin{displaymath}
\delta E = \frac{2\pi  \rho}{u} P = \frac{e^2}{3 \epsilon_0 
c^3} \frac{\gamma^4  u^3}{\rho}.
\end{displaymath}">|; 

$key = q/1slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="$1/r$">|; 

$key = q/mbox{{boldmath{{omega{}=(0,,0,,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$\mbox{\boldmath$\omega$} = (0, 0, \omega)$">|; 

$key = q/displaystyles_pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2358.png"
 ALT="$\displaystyle s_\pm$">|; 

$key = q/{displaymath}E_z(x,y)=E_0,sin(k_x,x),sin(k_y,y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2631.png"
 ALT="\begin{displaymath}
E_z(x,y) = E_0 \sin(k_x x) \sin(k_y y),
\end{displaymath}">|; 

$key = q/R^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="$R^{-1}$">|; 

$key = q/oint{{bf{curl},{{bf{A}cdotd{{bf{S}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$\oint{\bf curl} {\bf A}\cdot d{\bf S} = 0$">|; 

$key = q/{displaymath}{{bf{g}=epsilon_0,{{bf{E}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2167.png"
 ALT="\begin{displaymath}
{\bf g} = \epsilon_0 {\bf E}\times{\bf B}.
\end{displaymath}">|; 

$key = q/delta_{nn'}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1632.png"
 ALT="$\delta_{nn'} = 1$">|; 

$key = q/displaystyleleft.int_0^1x,y,dxright|_{y=0}+left.int_0^1x,y,dyright|_{x=1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle \left.\int_0^1 x y dx\right\vert _{y=0}+\left.\int_0^1 x y  dy
\right\vert _{x=1}$">|; 

$key = q/displaystylenabla^2W_z=-C_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle \nabla^2 W_z = - C_z,$">|; 

$key = q/displaystylehat{{bf{k}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2520.png"
 ALT="$\displaystyle \hat{\bf k}_t$">|; 

$key = q/{displaymath}{mitdiv},{{bf{h}=-c,frac{partialT}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="\begin{displaymath}
{\mit div} {\bf h} = -c \frac{\partial T}{\partial t}.
\end{displaymath}">|; 

$key = q/displaystyleE_r,hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2527.png"
 ALT="$\displaystyle E_r \hat{\bf y},$">|; 

$key = q/{displaymath}frac{4pi,epsilon_0}{e},{{bf{E}=frac{1}{s^2,r}left({{bf{r}-frac{r,{{ot{{bf{u}}{c}right)-frac{r}{s^2,c^2},dot{{bf{u},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="569" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3255.png"
 ALT="\begin{displaymath}
\frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{1}{s^2  r} \l...
...t\!\dot{\bf u}}{c}\right) - \frac{r}{s^2  c^2}  \dot{\bf u},
\end{displaymath}">|; 

$key = q/H_c=B_cslashmu=B_gslashmu=(mu_0slashmu),H_g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1841.png"
 ALT="$H_c = B_c/\mu = B_g/\mu = (\mu_0/\mu) H_g$">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{rho({{bf{r'},t-|{{bf{r}-{{bf{r'}|slashc)}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int \frac{\rho({\bf r'}, t- \vert{\bf r}
-{\bf r '}\vert/c)}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r'}$">|; 

$key = q/E_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3069.png"
 ALT="$E_x$">|; 

$key = q/displaystylea_x,(a_y,b_z-a_z,b_y)+a_y,(a_z,b_x-a_x,b_z)+a_z,(a_x,b_y-a_y,b_x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle a_x (a_y  b_z-a_z  b_y) + a_y  (a_z  b_x- a_x  b_z)
+a_z (a_x  b_y - a_y  b_x)$">|; 

$key = q/{displaymath}t'=C,x+D,t,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2709.png"
 ALT="\begin{displaymath}
t' = C  x + D  t,
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{epsilon_0}{2}intphi,nabla!cdot!{{bf{E},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="\begin{displaymath}
W =\frac{\epsilon_0}{2}\int\phi  \nabla\!\cdot\! {\bf E}  d^3{\bf r}.
\end{displaymath}">|; 

$key = q/d,{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2277.png"
 ALT="$d {\mit\Omega}$">|; 

$key = q/{{bf{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2110.png"
 ALT="${\bf u}$">|; 

$key = q/{{bf{grad},({mitdiv},{{bf{A});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="${\bf grad} ({\mit div} {\bf A})$">|; 

$key = q/{{bf{D}=epsilon_0,epsilon,{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1760.png"
 ALT="${\bf D} =\epsilon_0  \epsilon  {\bf E}$">|; 

$key = q/q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$q'$">|; 

$key = q/displaystylefrac{d{mbox{{boldmath{{rho{}}}{dt'}=u,(-sinphi,,cosphi,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3359.png"
 ALT="$\displaystyle \frac{d{\mbox{\boldmath$\rho$}}}{dt'}= u (-\sin\phi,  \cos\phi,  0),$">|; 

$key = q/{displaymath}y=A,y'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2702.png"
 ALT="\begin{displaymath}
y = A y'.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{E}_{{rm{rad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3274.png"
 ALT="$\displaystyle {\bf E}_{\rm rad}$">|; 

$key = q/{displaymath}q'=frac{a}{b},q,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1531.png"
 ALT="\begin{displaymath}
q' = \frac{a}{b} q,
\end{displaymath}">|; 

$key = q/v({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="$v({\bf r}, t)$">|; 

$key = q/dy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$dy$">|; 

$key = q/B_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2821.png"
 ALT="$B_i$">|; 

$key = q/{displaymath}V_2=V_1,frac{M}{L_1}exp(-R_1,tslashL_1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1933.png"
 ALT="\begin{displaymath}
V_2 = V_1  \frac{M}{L_1} \exp(- R_1  t/L_1).
\end{displaymath}">|; 

$key = q/{displaymath}frac{pi}{2}sum_{n=1}^inftyC_n,delta_{nn'}=frac{pi}{2},C_{n'}=int_0^piphi_0(y),sin(n',y),,dy,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1636.png"
 ALT="\begin{displaymath}
\frac{\pi}{2} \sum_{n=1}^\infty C_n  \delta_{n n'} = \frac{\pi}{2}  C_{n'} =
\int_0^\pi \phi_0(y) \sin (n'  y)  dy,
\end{displaymath}">|; 

$key = q/q'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1710.png"
 ALT="$q''$">|; 

$key = q/sin(n',y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1634.png"
 ALT="$\sin (n' y)$">|; 

$key = q/displaystylefrac{c,epsilon_0,E_0^{,2}}{2},hat{{bf{k}=c,langleUrangle,hat{{bf{k},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2152.png"
 ALT="$\displaystyle \frac{c \epsilon_0  E_0^{ 2}}{2}  \hat{\bf k}= c  \langle U\rangle  \hat{\bf k},$">|; 

$key = q/{displaymath}k^2,c^2=omega^2-frac{omega_p^{,2},omega}{omega+{{rm{i},nu}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2436.png"
 ALT="\begin{displaymath}
k^2 c^2 = \omega^2 - \frac{\omega_p^{ 2} \omega}{\omega + {\rm i} \nu}.
\end{displaymath}">|; 

$key = q/{displaymath}phi_1=phi_2{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1418.png"
 ALT="\begin{displaymath}
\phi_1 = \phi_2
\end{displaymath}">|; 

$key = q/Z_0=73;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2096.png"
 ALT="$Z_0 = 73$">|; 

$key = q/displaystylefrac{a}{a+b},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$\displaystyle \frac{a}{a+b},$">|; 

$key = q/{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="${\bf a}$">|; 

$key = q/d{{bf{S}=(0,,0,,dS_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$d{\bf S} = (0, 0, dS_z)$">|; 

$key = q/{displaymath}{mitPhi}_2=int_{{rm{loop,2}{{bf{B}_1cdotd{{bf{S}_2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1863.png"
 ALT="\begin{displaymath}
{\mit\Phi}_2 = \int_{\rm loop  2} {\bf B}_1\cdot d{\bf S}_2,
\end{displaymath}">|; 

$key = q/displaystyle0+int_0^1y,dy=frac{1}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle 0 + \int_0^1 y dy = \frac{1}{2}.$">|; 

$key = q/displaystylec_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle c_{x'}$">|; 

$key = q/(partialslashpartialx',partialslashpartialy',partialslashpartialz');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="$(\partial/\partial x', \partial/\partial y',
\partial/\partial z')$">|; 

$key = q/Deltatsimlslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2214.png"
 ALT="$\Delta t \sim l/c$">|; 

$key = q/{displaymath}phi_3=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1410.png"
 ALT="\begin{displaymath}
\phi_3 =0
\end{displaymath}">|; 

$key = q/{displaymath}V(0,t)=V_0,cos(omega,t).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2058.png"
 ALT="\begin{displaymath}
V(0, t) = V_0  \cos(\omega  t).
\end{displaymath}">|; 

$key = q/Z_{{rm{in}=Z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2102.png"
 ALT="$Z_{\rm in} = Z_0$">|; 

$key = q/bslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2103.png"
 ALT="$b/a$">|; 

$key = q/{displaymath}I_i=I_{0,i},frac{t}{T}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1984.png"
 ALT="\begin{displaymath}
I_i = I_{0 i}  \frac{t}{T}.
\end{displaymath}">|; 

$key = q/-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1650.png"
 ALT="$-2$">|; 

$key = q/{displaymath}nablacdot(phi_3,{{bf{E}_3)=-E_3^{~2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1447.png"
 ALT="\begin{displaymath}
\nabla\cdot (\phi_3  {\bf E}_3) = - E_3^{&nbsp;2}
\end{displaymath}">|; 

$key = q/theta_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2491.png"
 ALT="$\theta_i$">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=(a_y,b_z-a_z,b_y,,a_z,b_x-a_x,b_z,,a_x,b_y-a_y,b_x)={{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="438" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\begin{displaymath}
{\bf a}\times{\bf b} = (a_y   b_z-a_z  b_y,  a_z  b_x - a_x  b_z,  a_x  b_y - a_y  b_x)
={\bf c}.
\end{displaymath}">|; 

$key = q/{displaymath}P=-frac{e^2}{6pi,epsilon_0,c^3},A_muA^mu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3316.png"
 ALT="\begin{displaymath}
P = -\frac{e^2}{6\pi \epsilon_0  c^3}  A_\mu A^\mu,
\end{displaymath}">|; 

$key = q/{{bf{P}=epsilon_0,chi_e,{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1723.png"
 ALT="${\bf P}=\epsilon_0 
\chi_e  {\bf E}$">|; 

$key = q/{displaymath}frac{partial^2I}{partialx,partialt}=-C,frac{partial^2V}{partialt^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2053.png"
 ALT="\begin{displaymath}
\frac{\partial^2 I}{\partial x  \partial t} =
-C \frac{\partial^2 V}{\partial t^2}.
\end{displaymath}">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$A$">|; 

$key = q/{displaymath}{calF}_muU^mu=frac{e}{c},F_{munu},U^muU^nu=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3178.png"
 ALT="\begin{displaymath}
{\cal F}_\mu U^\mu = \frac{e}{c}  F_{\mu\nu}  U^\mu U^\nu = 0.
\end{displaymath}">|; 

$key = q/displaystyle|{{bf{r}-{{bf{r}'|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$\displaystyle \vert{\bf r} - {\bf r}'\vert$">|; 

$key = q/{displaymath}W=-frac{1}{2,mu_0}oint_S{{bf{A}times{{bf{B}cdotd{{bf{S}+frac{1}{2,mu_0}int_VB^2,dV,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1999.png"
 ALT="\begin{displaymath}
W = -\frac{1}{2 \mu_0} \oint_S {\bf A}\times{\bf B} \cdot d{\bf S} +
\frac{1}{2 \mu_0} \int_V B^2 dV,
\end{displaymath}">|; 

$key = q/I_0^{,2}R_{{rm{rad}slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2238.png"
 ALT="$I_0^{ 2}R_{\rm rad}/2$">|; 

$key = q/displaystylefrac{partialE_y}{partialx}-frac{partialE_x}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2582.png"
 ALT="$\displaystyle \frac{\partial E_y}{\partial x} - \frac{\partial E_x}{\partial y},$">|; 

$key = q/S_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$S_2$">|; 

$key = q/{displaymath}oint_C{{bf{A}cdotd{{bf{l}=int_S{{bf{curl,A}cdotd{{bf{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="\begin{displaymath}
\oint_C {\bf A}\cdot d{\bf l} = \int_S {\bf curl A}\cdot d{\bf S}
\end{displaymath}">|; 

$key = q/omega<omega_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2347.png"
 ALT="$\omega &lt; \omega_p$">|; 

$key = q/E_{{rm{sheet},A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$E_{\rm sheet} A$">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$n$">|; 

$key = q/oint{{bf{A}cdotd{{bf{l}=I_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$\oint {\bf A}\cdot d{\bf l}
= I_{\rm max}$">|; 

$key = q/{displaymath}W=qint_P^Q{{bf{E}cdotd{{bf{l}=-qint_P^Qnablaphicdotd{{bf{l}=-qleft[,phi(Q)-phi(P),right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="450" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="\begin{displaymath}
W = q \int_P^Q {\bf E}\cdot d{\bf l} = - q\int_P^Q \nabla\phi\cdot d{\bf l}
= -q \left[ \phi(Q)- \phi(P) \right].
\end{displaymath}">|; 

$key = q/{displaymath}phi_m(r,theta)=-(B_1slashmu),r,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1823.png"
 ALT="\begin{displaymath}
\phi_m(r,\theta) = - (B_1/\mu) r \cos\theta.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=E_0,sin(omega,t),hat{{bf{z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2272.png"
 ALT="\begin{displaymath}
{\bf E} = E_0 \sin(\omega t) \hat{\bf z}.
\end{displaymath}">|; 

$key = q/{displaymath}int_{-1}^{+1}frac{(1-mu^2),dmu}{[1-(uslashc),mu]^5}=frac{4}{3},gamma^6.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3353.png"
 ALT="\begin{displaymath}
\int_{-1}^{+1}\frac{(1-\mu^2) d\mu}{[1-(u/c) \mu]^5} = \frac{4}{3} \gamma^6.
\end{displaymath}">|; 

$key = q/displaystyledot{{bf{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3360.png"
 ALT="$\displaystyle \dot{\bf u}$">|; 

$key = q/{displaymath}k_{pm}^{,2},c^2=omega^2left[1-frac{omega_p^{,2}}{omega,(omegapm{mitOmega})}right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img2376.png"
 ALT="\begin{displaymath}
k_{\pm}^{ 2} c^2 = \omega^2\left[1- \frac{\omega_p^{ 2}}{\omega (\omega\pm{\mit \Omega})}\right],
\end{displaymath}">|; 

$key = q/displaystylemu_0,{{bf{j}+epsilon,epsilon_0mu_0,frac{partial{{bf{E}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2396.png"
 ALT="$\displaystyle \mu_0 {\bf j} + \epsilon \epsilon_0\mu_0 \frac{\partial {\bf E}}{\partial t},$">|; 

$key = q/r=sqrt{x^2+y^2+z^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2990.png"
 ALT="$r=\sqrt{x^2+y^2+z^2}$">|; 

$key = q/{{bf{p}=q,{{bf{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1656.png"
 ALT="${\bf p} = q  {\bf d}$">|; 

$key = q/A_{i'j'cdotsk'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2790.png"
 ALT="$A_{i'j'\cdots k'}$">|; 

$key = q/alpha=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3371.png"
 ALT="$\alpha=\pi/2$">|; 

$key = q/phi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1399.png"
 ALT="$\phi_2$">|; 

$key = q/{{bf{j}({{bf{r})cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="${\bf j}({\bf r})
\cdot d{\bf S}$">|; 

$key = q/{displaymath}{r'}^2=r^2+c^2,{t'}^2=r^2+frac{gamma^2,u^2,x^2}{c^2}=r^2left(1+frac{gamma^2,u_r^{~2}}{c^2}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img3140.png"
 ALT="\begin{displaymath}
{r'}^2 = r^2 + c^2  {t'}^2 = r^2 +\frac{ \gamma^2  u^2  x^2}{c^2}
= r^2\left(1 + \frac{\gamma^2  u_r^{&nbsp;2}}{c^2}\right).
\end{displaymath}">|; 

$key = q/6,{{rm{cm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2416.png"
 ALT="$6 {\rm cm}$">|; 

$key = q/displaystyle{{bf{E}({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="$\displaystyle {\bf E}({\bf r})$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="\begin{displaymath}
\left(\nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right)
G=0.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial^2V}{partialx^2}=-L,frac{partial^2I}{partialx,partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2052.png"
 ALT="\begin{displaymath}
\frac{\partial^2 V}{\partial x^2} = - L  \frac{\partial^2 I}{\partial x  \partial t}.
\end{displaymath}">|; 

$key = q/displaystylefrac{3,mu,B_0}{mu+2,mu_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1828.png"
 ALT="$\displaystyle \frac{3 \mu B_0}{\mu+2 \mu_0}.$">|; 

$key = q/{displaymath}V(x,t)=V_0,exp[{{rm{i},(omega,t-k,x)]+K,V_0,exp[{{rm{i},(omega,t+k,x)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2077.png"
 ALT="\begin{displaymath}
V(x, t) = V_0  \exp[{\rm i} (\omega  t - k x)] + K  V_0   \exp[{\rm i} (\omega  t + k x)].
\end{displaymath}">|; 

$key = q/x=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1590.png"
 ALT="$x= r \cos\theta$">|; 

$key = q/{{bf{u}'=(u'_1,u'_2,u'_3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2755.png"
 ALT="${\bf u}' = (u'_1, u'_2, u'_3)$">|; 

$key = q/{displaymath}n,{{bf{a}equiv(n,a_x,,n,a_y,,n,a_z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{displaymath}
n {\bf a} \equiv (n a_x,  n a_y,  n a_z).
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}+{{bf{c})={{bf{a}times{{bf{b}+{{bf{a}times{{bf{c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b} +{\bf c})= {\bf a} \times{\bf b}+{\bf a}\times{\bf c},
\end{displaymath}">|; 

$key = q/Q=rho({{bf{r}),dx,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$Q=\rho({\bf r}) dx dy dz$">|; 

$key = q/z+dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1664.png"
 ALT="$z+dz$">|; 

$key = q/displaystyle{{rm{i},{{bf{k}cdot{{bf{A}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="$\displaystyle {\rm i}  {\bf k}\cdot {\bf A}.$">|; 

$key = q/{displaymath}Boxequivpartial_mupartial^mu=-nabla^2+frac{1}{c^2}frac{partial^2}{partialt^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2913.png"
 ALT="\begin{displaymath}
\Box \equiv \partial_\mu \partial^\mu = -\nabla^2 + \frac{1}{c^2} \frac
{\partial^2}{\partial t^2}.
\end{displaymath}">|; 

$key = q/{mitPhi}_2=N_2,l,mu_0N_1,I_1,pi,r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1909.png"
 ALT="${\mit\Phi}_2 = N_2  l  \mu_0 N_1 
I_1 \pi  r^2$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,{{bf{j}+lambda,frac{partial{{bf{E}}{partialt}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0  {\bf j} +\lambda \frac{\partial {\bf E}}{\partial t}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{B}=-frac{mu_0,e,gamma}{4pi,{r'}^3},{{bf{u}times{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3136.png"
 ALT="\begin{displaymath}
{\bf B} = -\frac{\mu_0 e \gamma}{4\pi {r'}^3}  {\bf u}\times{\bf r}.
\end{displaymath}">|; 

$key = q/V,I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1943.png"
 ALT="$V I$">|; 

$key = q/int_S{{bf{j}cdotd{{bf{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="$\int_S {\bf j} \cdot d{\bf S} $">|; 

$key = q/{displaymath}E_perp=E_z(z=0_+)=-frac{partialphi(z=0_+)}{partialz}=-frac{partialphi_{{rm{analogue}(z=0_+)}{partialz},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1497.png"
 ALT="\begin{displaymath}
E_\perp = E_z(z=0_+) = - \frac{\partial \phi(z=0_+)}{\partial z}
= - \frac{\partial \phi_{\rm analogue}(z=0_+)}{\partial z},
\end{displaymath}">|; 

$key = q/{{bf{a}times({{bf{b}times{{bf{c})=(a_y,b_x,c_y,,-a_x,b_x,c_y,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="${\bf a}\times({\bf b}\times{\bf c}) = (a_y  b_x  c_y,  -a_x  b_x  c_y,  0)$">|; 

$key = q/{displaymath}epsilon=1+chi_e{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1684.png"
 ALT="\begin{displaymath}
\epsilon= 1 + \chi_e
\end{displaymath}">|; 

$key = q/{displaymath}frac{c}{2}left(B_{ab}-B_{ba}right)=-partial_a{mitPhi}_b+partial_b{mitPhi}_a,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3027.png"
 ALT="\begin{displaymath}
\frac{c}{2} \left(B_{ab} - B_{ba}\right) = - \partial_a {\mit \Phi}_b
+\partial_b{\mit \Phi}_a,
\end{displaymath}">|; 

$key = q/displaystyleleft(frac{partialV}{partialx},frac{partialV}{partialy}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1568.png"
 ALT="$\displaystyle \left( \frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}
\right).$">|; 

$key = q/1slashgamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3380.png"
 ALT="$1/\gamma$">|; 

$key = q/{displaymath}oint_S{{bf{D}!cdot!d{{bf{S}=int_Vrho_f,dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1680.png"
 ALT="\begin{displaymath}
\oint_S {\bf D}\!\cdot\!d{\bf S} = \int_V \rho_f dV.
\end{displaymath}">|; 

$key = q/{displaymath}partial_jG^{ji}+partial_4G^{4i}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3087.png"
 ALT="\begin{displaymath}
\partial_j G^{ji} + \partial_4 G^{4i} = 0.
\end{displaymath}">|; 

$key = q/displaystyleW_x({{bf{r});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$\displaystyle W_x({\bf r} )$">|; 

$key = q/dT=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$dT=0$">|; 

$key = q/{displaymath}int_{-infty}^{infty}g,frac{partialf}{partialx},dx=-int_{-infty}^{infty}f,frac{partialg}{partialx},dx.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty} g  \frac{\partial f}{\partial x} d...
...\int_{-\infty}^{\infty} f  \frac{\partial g}{\partial x} dx.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{B}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="$\nabla\cdot{\bf B}
\neq 0$">|; 

$key = q/displaystyleF^{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3042.png"
 ALT="$\displaystyle F^{i4}$">|; 

$key = q/{displaymath}G^{munu}=leftlgrouparray{{cccc}0&-E_z&+E_y&-c,B_x[0.5ex]+E_z&0&-E_xz[0.5ex]+c,B_x&+c,B_y&+c,B_z&0array{rightrgroup.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="111" BORDER="0"
 SRC="|."$dir".q|img3068.png"
 ALT="\begin{displaymath}
G^{\mu\nu} = \left\lgroup \begin{array}{cccc}
0 &amp; -E_z &amp; +E_...
....5ex]
+c B_x &amp;+ c B_y &amp;+c B_z &amp; 0\end{array}\right
\rgroup.
\end{displaymath}">|; 

$key = q/{{bf{u}=(u,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3103.png"
 ALT="${\bf u} = (u,0,0)$">|; 

$key = q/d{{bf{l}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1979.png"
 ALT="$d{\bf l}_i$">|; 

$key = q/textstyleleft(frac{2,epsilon_2}{epsilon_2+epsilon_1}right)q.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1721.png"
 ALT="$\textstyle \left(\frac{2 \epsilon_2}{\epsilon_2+\epsilon_1}\right) q.$">|; 

$key = q/displaystyleB_{perp,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2499.png"
 ALT="$\displaystyle B_{\perp 2}.$">|; 

$key = q/gamma(u);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2936.png"
 ALT="$\gamma(u)$">|; 

$key = q/B_{ij}=-B_{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3029.png"
 ALT="$B_{ij} = -B_{ji}$">|; 

$key = q/displaystylefrac{partialV}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1558.png"
 ALT="$\displaystyle \frac{\partial V}{\partial y},$">|; 

$key = q/b>a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1522.png"
 ALT="$b&gt;a$">|; 

$key = q/(partialhslashpartialx)_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$(\partial h/\partial x)_y$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r'})}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi } \int \frac{{\bf j}({\bf r'})}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r'}.$">|; 

$key = q/{displaymath}v_p=frac{omega}{k}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img2330.png"
 ALT="\begin{displaymath}
v_p = \frac{\omega}{k}.
\end{displaymath}">|; 

$key = q/0leqyleqpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1603.png"
 ALT="$0\leq y \leq \pi$">|; 

$key = q/|b|=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\vert b\vert=0$">|; 

$key = q/{displaymath}A_{kcdotsl,mn}^{icdotsj}=frac{partialA_{kcdotsl}^{icdotsj}}{partialx^mpartialx^n}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img2828.png"
 ALT="\begin{displaymath}
A_{k\cdots l,mn}^{i\cdots j} =\frac{\partial A_{k\cdots l}^{i\cdots j} }
{\partial x^m \partial x^n}
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{P}=epsilon_0,chi_e,{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1681.png"
 ALT="\begin{displaymath}
{\bf P} = \epsilon_0 \chi_e  {\bf E},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}'!cdot!{{bf{j}_t=frac{j_t^{~2}}{sigma}-{{bf{E}!cdot!{{bf{j}_t.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1847.png"
 ALT="\begin{displaymath}
{\bf E}'\!\cdot\!{\bf j}_t = \frac{j_t^{&nbsp;2}}{\sigma}
-{\bf E}\!\cdot\!{\bf j}_t.
\end{displaymath}">|; 

$key = q/{displaymath}frac{{{bf{f}!cdot!{{bf{u}}{c}=frac{e}{c},{{bf{E}!cdot!{{bf{u}=frac{E_i,u^i=frac{e}{gamma,c}(F_{4i},U^i+F_{44},U^4).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3175.png"
 ALT="\begin{displaymath}
\frac{{\bf f}\!\cdot\!{\bf u}}{c} = \frac{e}{c}  {\bf E}\!\...
...E_i  u^i = \frac{e}{\gamma c}
(F_{4i}  U^i + F_{44}  U^4).
\end{displaymath}">|; 

$key = q/{{bf{E}_0cdot{{bf{k}={{bf{B}_0cdot{{bf{k}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2440.png"
 ALT="${\bf E}_0\cdot{\bf k} = {\bf B}_0\cdot{\bf k} = 0$">|; 

$key = q/displaystyleleft(frac{partial^2}{partialx^2}+frac{partial^2}{partialy^2}right)!B_z+left(frac{omega^2}{c^2}-k^2right)!B_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2599.png"
 ALT="$\displaystyle \left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}\right)\!
B_z + \left(\frac{\omega^2}{c^2}-k^2\right)\!B_z$">|; 

$key = q/{displaymath}d^4x'={calJ},d^4x,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2937.png"
 ALT="\begin{displaymath}
d^4 x' = {\cal J}  d^4 x,
\end{displaymath}">|; 

$key = q/{displaymath}theta_B=tan^{-1}left(frac{n_2}{n_1}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2570.png"
 ALT="\begin{displaymath}
\theta_B = \tan^{-1}\left(\frac{n_2}{n_1}\right).
\end{displaymath}">|; 

$key = q/displaystyleBox^2{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="$\displaystyle \Box^2 {\bf B}$">|; 

$key = q/{displaymath}frac{partialt'}{partialt}=frac{1}{1-{{bf{r}!cdot!{{bf{u}slashr,c}=frac{r}{s},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img3246.png"
 ALT="\begin{displaymath}
\frac{\partial t'}{\partial t} = \frac{1}{1- {\bf r}\!\cdot\!
{\bf u}/r c} = \frac{r}{s},
\end{displaymath}">|; 

$key = q/phi_mrightarrow-(B_0slashmu_0),r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1818.png"
 ALT="$\phi_m \rightarrow - (B_0/\mu_0) r \cos\theta$">|; 

$key = q/{displaymath}W=-frac{1}{4pi,epsilon_0}frac{q^2}{4,d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1515.png"
 ALT="\begin{displaymath}
W = - \frac{1}{4\pi  \epsilon_0} \frac{q^2}{4 d}.
\end{displaymath}">|; 

$key = q/|F|,|r|,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\vert F\vert \vert r\vert \sin\theta$">|; 

$key = q/{displaymath}B_y={{rm{i},left(frac{omega}{c^2}frac{partialE_z}{partialx}+k,frac{ly}right)left(frac{omega^2}{c^2}-k^2right)^{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2590.png"
 ALT="\begin{displaymath}
B_y = {\rm i} \left(\frac{\omega}{c^2}\frac{\partial E_z}{\...
...{\partial y}\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1}.
\end{displaymath}">|; 

$key = q/{displaymath}overline{z}=frac{pi,a^4}{4}frac{3}{2pi,a^3}=frac{3,a}{8}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="\begin{displaymath}
\overline{z} = \frac{ \pi  a^4}{4}\frac{3}{2\pi  a^3}= \frac{3 a}{8}.
\end{displaymath}">|; 

$key = q/{displaymath}{mitdiv},{{bf{A}=nablacdot{{bf{A}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="\begin{displaymath}
{\mit div} {\bf A} = \nabla\cdot {\bf A}
\end{displaymath}">|; 

$key = q/x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$x'$">|; 

$key = q/displaystylenabla^2A_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$\displaystyle \nabla^2 A_x$">|; 

$key = q/{displaymath}{{bf{R}={{bf{r}-{{bf{r}',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="\begin{displaymath}
{\bf R} = {\bf r} - {\bf r}',
\end{displaymath}">|; 

$key = q/dt^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2683.png"
 ALT="$dt^2$">|; 

$key = q/{displaymath}left(nabla^2-frac{1}{c^2}frac{partial^2}{partialt^2}right)G({{bf{r}f{r}';t,t')=delta({{bf{r}-{{bf{r'}),delta(t-t').{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="\begin{displaymath}
\left(\nabla^2- \frac{1}{c^2}\frac{\partial^2}{\partial t^2}...
..., {\bf r}'; t, t')= \delta({\bf r} - {\bf r'})  \delta(t-t').
\end{displaymath}">|; 

$key = q/{displaymath}ds^2=g_{ij},dx^i,dx^j,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2829.png"
 ALT="\begin{displaymath}
ds^2 = g_{ij}  dx^i  dx^j,
\end{displaymath}">|; 

$key = q/displaystylemu_0,{{bf{j}+epsilon_0mu_0,frac{partial{{bf{E}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2176.png"
 ALT="$\displaystyle \mu_0 {\bf j} + \epsilon_0\mu_0  \frac{\partial {\bf E}}{\partial t}.$">|; 

$key = q/L,dIslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1894.png"
 ALT="$L  dI/dt$">|; 

$key = q/displaystylev_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle v_x$">|; 

$key = q/displaystyle{{bf{E}_perp';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3097.png"
 ALT="$\displaystyle {\bf E}_\perp'$">|; 

$key = q/{displaymath}E_i=-partial_i{mitPhi}_4+partial_4{mitPhi}_i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img3023.png"
 ALT="\begin{displaymath}
E_i = -\partial_i {\mit \Phi}_4 +\partial_4 {\mit \Phi}_i.
\end{displaymath}">|; 

$key = q/{displaymath}M_{21}=frac{mu_0}{4pi}oint_{{rm{loop,1}oint_{{rm{loop,2}frac{d{{bf{l}_1cdotd{{bf{l}_2}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1879.png"
 ALT="\begin{displaymath}
M_{21} = \frac{\mu_0}{4\pi}
\oint_{\rm loop  1}\oint_{\rm ...
...frac{d{\bf l}_1\cdot d{\bf l}_2}{\vert{\bf r}-
{\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/mu=mu({{bf{H});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1799.png"
 ALT="$\mu = \mu({\bf H})$">|; 

$key = q/{displaymath}phi({{bf{r})rightarrow0mbox{hspace{1cm}as~{|{{bf{r}|rightarrowinfty{},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="\begin{displaymath}
\phi({\bf r}) \rightarrow 0 \mbox{\hspace{1cm} as&nbsp;$\vert{\bf r}\vert\rightarrow \infty$},
\end{displaymath}">|; 

$key = q/{displaymath}u({{bf{r})rightarrow0mbox{hspace{1cm}as{|{{bf{r}|rightarrowinfty{},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="\begin{displaymath}
u({\bf r}) \rightarrow 0 \mbox{\hspace{1cm} as $\vert{\bf r}\vert\rightarrow\infty$},
\end{displaymath}">|; 

$key = q/{displaymath}[rho]simeqrho+frac{partialrho}{partialt},(t_r-t)+frac{1}{2}frac{partial^2rho}{partialt^2},(t_r-t)^2+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="\begin{displaymath}[\rho]\simeq \rho + \frac{\partial\rho}{\partial t}  (t_r-t)...
...}{2} \frac{\partial^2 \rho}{\partial t^2} (t_r -t )^2+\cdots,
\end{displaymath}">|; 

$key = q/I,R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1893.png"
 ALT="$I R$">|; 

$key = q/{displaymath}int_VE_3^{~2},dV=-sum_{i=1}^Noint_{S_i}phi_3,{{bf{E}_3cdotd{{bf{S}_i-oint_Sphi_3,{{bf{E}_3cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1448.png"
 ALT="\begin{displaymath}
\int_V E_3^{&nbsp;2} dV = - \sum_{i=1}^N \oint_{S_i} \phi_3 {\bf E}_3\cdot d{\bf S}_i
-\oint_S \phi_3 {\bf E}_3\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=E_0,{{rm{e}^{,{{rm{i},(k,x-omega,t)},hat{{bf{z},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2329.png"
 ALT="\begin{displaymath}
{\bf E} = E_0 {\rm e}^{ {\rm i} (k x-\omega t)} \hat{\bf z},
\end{displaymath}">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$f$">|; 

$key = q/{{bf{e}_yequiv(0,1,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="${\bf e}_y \equiv (0,1,0)$">|; 

$key = q/{displaymath}phi=frac{q}{4pi,epsilon_0},frac{1}{[(x-b)^2+y^2+z^2]^{1slash2}}-fra,epsilon_0}frac{1}{[(x-c)^2+y^2+z^2]^{1slash2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1525.png"
 ALT="\begin{displaymath}
\phi = \frac{q}{4\pi \epsilon_0} \frac{1}{[(x-b)^2+y^2+z^2...
...\frac{q'}{4\pi \epsilon_0}
\frac{1}{[(x-c)^2+y^2+z^2]^{1/2}}.
\end{displaymath}">|; 

$key = q/v_1slashv_2=n_2slashn_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2471.png"
 ALT="$v_1/v_2=n_2/n_1$">|; 

$key = q/rho_0=e,n_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2958.png"
 ALT="$\rho_0=e n_0$">|; 

$key = q/Q^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3296.png"
 ALT="$
Q^{\mu\nu}$">|; 

$key = q/{displaymath}(AB)^2=(OA)^2+(OB)^2-2,(OA),(OB),costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="\begin{displaymath}
(AB)^2 = (OA)^2 + (OB)^2 - 2  (OA) (OB) \cos\theta,
\end{displaymath}">|; 

$key = q/B_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="$B_\perp$">|; 

$key = q/x^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2874.png"
 ALT="$x^4$">|; 

$key = q/{displaymath}G^{ij}=-epsilon^{ijk},E_k=-frac{1}{2},epsilon^{ijk}epsilon_{kab},E^{ab}=-E^{ij}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3063.png"
 ALT="\begin{displaymath}
G^{ij} = -\epsilon^{ijk}  E_k =-\frac{1}{2} \epsilon^{ijk} \epsilon_{kab}
 E^{ab} = - E^{ij}.
\end{displaymath}">|; 

$key = q/r=sqrt{x^2+y^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$r=\sqrt{x^2+y^2}$">|; 

$key = q/{displaymath}partial_muT^mu=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3284.png"
 ALT="\begin{displaymath}
\partial_\mu T^\mu = 0,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=(a_y,b_z-a_z,b_y,,a_z,b_x-a_x,b_z,,a_x,b_y-a_y,b_x){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="\begin{displaymath}
{\bf a}\times{\bf b} = (a_y  b_z-a_z  b_y,  a_z  b_x-a_x  b_z,  a_x  b_y-a_y  b_x)
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{E}_3=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1439.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf E}_3 = 0
\end{displaymath}">|; 

$key = q/{displaymath}x^2+y^2+z^2-c^2,t^2=x'^2+y'^2+z'^2-c^2,t'^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2699.png"
 ALT="\begin{displaymath}
x^2 + y^2 + z^2 -c^2  t^2 = x'^2 + y'^2 + z'^2 - c^2  t'^2.
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial^2phi}{partialx^2}+frac{partial^2phi}{partialy^2}+frac{^2phi}{partialz^2}=-frac{rho(x,y,z)}{epsilon_0},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1472.png"
 ALT="\begin{displaymath}
\frac{\partial^2\phi}{\partial x^2} +\frac{\partial^2\phi}{\...
...artial^2\phi}{\partial z^2} = -\frac{\rho(x,y,z)}{\epsilon_0},
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig14.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig14.eps}}
\end{figure}">|; 

$key = q/displaystyleint_0^T(R_1,I_1^{,2}+R_2,I_2^{,2}),dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1963.png"
 ALT="$\displaystyle \int_0^T (R_1  I_1^{ 2} + R_2  I_2^{ 2} ) dt$">|; 

$key = q/{displaymath}frac{d^2phi}{dx^2}=frac{I}{epsilon_0,A}left(frac{m_e}{2,e}right)^{1slash2}phi^{-1slash2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1482.png"
 ALT="\begin{displaymath}
\frac{d^2\phi}{dx^2} = \frac{I}{\epsilon_0 A}\left(\frac{m_e}{2 e}\right)^{1/2}\phi^{-1/2}.
\end{displaymath}">|; 

$key = q/textstylesimeq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="$\textstyle \simeq$">|; 

$key = q/{displaymath}m,frac{d^2z}{dt^2}=qleft(E-vBright),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="\begin{displaymath}
m  \frac{d^2 z}{dt^2} = q\left(E - v B\right),
\end{displaymath}">|; 

$key = q/nabla^2phi_3=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1413.png"
 ALT="$\nabla^2\phi_3 = 0$">|; 

$key = q/dx^islashds;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2848.png"
 ALT="$dx^i/ds$">|; 

$key = q/{{bf{u}=u^i=dx^islashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2876.png"
 ALT="${\bf u} = u^i = dx^i/dt$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{rho({{bf{r}',t')}{4pi,epsilon_0}frac{delta(t-t'+|{{bf{r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{\rho({\bf r}' ,t ')} {4\pi  \epsil...
...vert{\bf r} - {\bf r}'\vert/c)}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{displaymath}phi_{{rm{analogue}rightarrow0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1491.png"
 ALT="\begin{displaymath}
\phi_{\rm analogue}\rightarrow 0
\end{displaymath}">|; 

$key = q/{displaymath}U=frac{B^2}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1975.png"
 ALT="\begin{displaymath}
U = \frac{B^2}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/n^r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2769.png"
 ALT="$n^r$">|; 

$key = q/dl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$dl$">|; 

$key = q/displaystyle-epsilon_0,(nablacdot{{bf{E}),{{bf{E}-frac{1}{mu_0}(nablacdot{{bf{B}),{{bf{B}+rho,{{bf{E}+{{bf{j}times{{bf{B}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2181.png"
 ALT="$\displaystyle - \epsilon_0 (\nabla\cdot {\bf E})  {\bf E} - \frac{1}{\mu_0}(\nabla\cdot {\bf B})  {\bf B}+
\rho {\bf E}+{\bf j}\times {\bf B}.$">|; 

$key = q/displaystylez.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle z.$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig37.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="230" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig37.eps}}
\end{figure}">|; 

$key = q/{displaymath}nablatimesnablatimes{{bf{B}=nabla(nablacdot{{bf{B})-nabla^2{{bf{B}=0mu_0,frac{partial,nablatimes{{bf{E}}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="472" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="\begin{displaymath}
\nabla\times\nabla\times{\bf B} = \nabla(\nabla\cdot{\bf B})...
...on_0\mu_0 \frac{\partial  \nabla\times {\bf E}}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}f=m_0,gamma^3,frac{du}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3155.png"
 ALT="\begin{displaymath}
f = m_0 \gamma^3 \frac{du}{dt},
\end{displaymath}">|; 

$key = q/-I_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="$-I_i$">|; 

$key = q/{displaymath}{{bf{E}_{{rm{radiation}=frac{e}{4pi,epsilon_0,c^2}frac{{{bf{r}times({{bf{r}_utimesdot{{bf{u})}{s^3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img3270.png"
 ALT="\begin{displaymath}
{\bf E}_{\rm radiation} = \frac{e}{4\pi \epsilon_0  c^2} \frac{{\bf r}\times
({\bf r}_u\times\dot{\bf u})}{s^3},
\end{displaymath}">|; 

$key = q/t=T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1947.png"
 ALT="$t=T$">|; 

$key = q/displaystylefrac{1}{4pi}intfrac{C_z({{bf{r'})}{|{{bf{r}-{{bf{r'}|},d^3{{bf{r'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="$\displaystyle \frac{1}{4\pi } \int\frac{C_z({\bf r'})}
{\vert{\bf r} - {\bf r'}\vert} d^3{\bf r'}.$">|; 

$key = q/{displaymath}nabla^2U=0,~~~nabla^2W_i=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="\begin{displaymath}
\nabla^2 U = 0,&nbsp;&nbsp;&nbsp;\nabla^2 W_i =0,
\end{displaymath}">|; 

$key = q/(r,theta,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1709.png"
 ALT="$(r, \theta, z)$">|; 

$key = q/{displaymath}{{bf{D}=epsilon_0,{{bf{E}+{{bf{P}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1679.png"
 ALT="\begin{displaymath}
{\bf D} = \epsilon_0  {\bf E} + {\bf P}
\end{displaymath}">|; 

$key = q/{displaymath}Z_{{rm{in}=frac{Z_0^{,2}}{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2092.png"
 ALT="\begin{displaymath}
Z_{\rm in} = \frac{Z_0^{ 2}}{R}.
\end{displaymath}">|; 

$key = q/{{bf{r}neq{{bf{r'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="${\bf r} \neq {\bf r'}$">|; 

$key = q/{displaymath}int_{-infty}^{infty}f(x),delta(x),dx=f(0)int_{-infty}^{infty}delta(x),dx=f(0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="\begin{displaymath}
\int_{-\infty}^{\infty}f(x)  \delta(x) dx = f(0)\int_{-\infty}^{\infty} \delta(x)
 dx = f(0),
\end{displaymath}">|; 

$key = q/{displaymath}{mitPhi}=int_a^bB_theta,dr=frac{mu_0,I}{2pi}ln(bslasha).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img2068.png"
 ALT="\begin{displaymath}
{\mit\Phi} = \int_a^b B_\theta  dr = \frac{\mu_0  I}{2\pi} \ln(b/a).
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{p}=-e,z,,hat{{bf{z}=-p_0,sin(omega,t),hat{{bf{z},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2275.png"
 ALT="\begin{displaymath}
{\bf p} = - e z  \hat{\bf z} = -p_0 \sin(\omega t) \hat{\bf z},
\end{displaymath}">|; 

$key = q/{displaymath}[rho,{{bf{E}+{{bf{j}times{{bf{B}]_i=frac{partialT_{ij}}{partialx_j}ialt}left[epsilon_0,{{bf{E}times{{bf{B}right]_i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2196.png"
 ALT="\begin{displaymath}[\rho {\bf E} + {\bf j}\times{\bf B}]_i = \frac {\partial T_...
...l}{\partial t}\left[\epsilon_0 {\bf E}\times{\bf B}\right]_i,
\end{displaymath}">|; 

$key = q/[A]equivA({{bf{r}',t-Rslashc);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="$[A] \equiv A({\bf r}', t-R/c)$">|; 

$key = q/{displaymath}omega^2=k^2,c^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2638.png"
 ALT="\begin{displaymath}
\omega^2= k^2 c^2,
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{a}'simeq{{bf{a}+deltatheta_z,{{bf{e}_ztimes{{bf{a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="\begin{displaymath}
{\bf a}' \simeq {\bf a} +\delta\theta_z  {\bf e}_z\times {\bf a},
\end{displaymath}">|; 

$key = q/G^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3058.png"
 ALT="$G^{\mu\nu}$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=nablatimesnablatimes{{bf{A}=nabla(nablacdot{{bf{A})-nabla^2{{bf{A}=-nabla^2{{bf{A},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \nabla\times\nabla\times {\bf A} = \nabla(\nabla\cdot{\bf A})
-\nabla^2{\bf A} = - \nabla^2{\bf A},
\end{displaymath}">|; 

$key = q/displaystylefrac{mu-mu_0}{mu+2,mu_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1826.png"
 ALT="$\displaystyle \frac{\mu-\mu_0}{\mu+2 \mu_0},$">|; 

$key = q/{displaymath}intleft[(nablatimes{{bf{U})^2-{{bf{U}cdotnablatimesnablatimes{{bf{Uvint{{bf{U}times(nablatimes{{bf{U})cdot{{bf{dS}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="487" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img1462.png"
 ALT="\begin{displaymath}
\int\left[(\nabla\times{\bf U})^2 - {\bf U}\cdot\nabla\times...
... \equiv \int {\bf U}\times(\nabla\times{\bf U})\cdot {\bf dS}.
\end{displaymath}">|; 

$key = q/displaystylefrac{Q_{{rm{total}}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1434.png"
 ALT="$\displaystyle \frac{Q_{\rm total}}{\epsilon_0},$">|; 

$key = q/E_{perp,A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="$E_{\perp A}$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$Q$">|; 

$key = q/{displaymath}s_pm=frac{e,E_pm}{m_e,omega,(omegapm{mitOmega})},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2363.png"
 ALT="\begin{displaymath}
s_\pm = \frac{e E_\pm}{m_e \omega (\omega\pm{\mit \Omega})},
\end{displaymath}">|; 

$key = q/displaystyleE_r=left(frac{1-alpha,beta}{1+alpha,beta}right)E_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2541.png"
 ALT="$\displaystyle E_r = \left(\frac{1-\alpha \beta}{1+\alpha \beta}\right) E_i,$">|; 

$key = q/displaystylez^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1537.png"
 ALT="$\displaystyle z^2,$">|; 

$key = q/209.0times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1792.png"
 ALT="$209.0\times 10^{-8}$">|; 

$key = q/displaystyle+left(frac{3(x-x')^2-|{{bf{r}-{{bf{r}'|^2}{|{{bf{r}-{{bf{r}'|^4}righac{F'}{c}+frac{(x-x')^2}{|{{bf{r}-{{bf{r}'|^3}frac{F''}{c^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$\displaystyle +\left(\frac{3(x-x')^2 - \vert{\bf r} - {\bf r}'\vert^2}{\vert{\b...
...frac{ F'}{c} + \frac{(x-x')^2}{\vert{\bf r} - {\bf r}'\vert^3} \frac{F''}{c^2},$">|; 

$key = q/int_{-infty}^{infty}delta(x),dx=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$\int_{-\infty}^{\infty} \delta(x) dx = 1$">|; 

$key = q/I_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="$I_1$">|; 

$key = q/A_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2806.png"
 ALT="$A_{ij}$">|; 

$key = q/nabla^2T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$\nabla^2 T$">|; 

$key = q/displaystylefrac{1}{pm(1-v^2slashc^2)^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2714.png"
 ALT="$\displaystyle \frac{1}{\pm (1-v^2/c^2)^{1/2}},$">|; 

$key = q/{displaymath}oint{{bf{A}cdotd{{bf{l}={{bf{curl},{{bf{A}cdotd{{bf{S}=|{{bf{curl},{{bf{A}|,|dS|,costheta,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="\begin{displaymath}
\oint {\bf A}\cdot d{\bf l} = {\bf curl} {\bf A} \cdot d{\b...
... =
\vert{\bf curl} {\bf A}\vert \vert d S\vert \cos\theta,
\end{displaymath}">|; 

$key = q/{{bf{grad},h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="${\bf grad} h$">|; 

$key = q/T^mu=A_nu,Q^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3299.png"
 ALT="$T^\mu = A_\nu  Q^{\mu\nu}$">|; 

$key = q/displaystyle{{rm{i},omega,B_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2577.png"
 ALT="$\displaystyle {\rm i} \omega  B_x$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\omega$">|; 

$key = q/{displaymath}C=frac{sigma,A}{V}=frac{epsilon_0,A}{d}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="\begin{displaymath}
C = \frac{\sigma A}{V} = \frac{\epsilon_0 A}{d}.
\end{displaymath}">|; 

$key = q/{displaymath}W_{{rm{analogue}=2,frac{epsilon_0}{2}int_{z>0}E^2_{{rm{analogue},dV.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img1510.png"
 ALT="\begin{displaymath}
W_{\rm analogue} = 2  \frac{\epsilon_0}{2} \int_{z&gt;0} E^2_{\rm analogue}  dV.
\end{displaymath}">|; 

$key = q/{displaymath}R=frac{I_r}{I_i}=left(frac{E_r}{E_i}right)^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2483.png"
 ALT="\begin{displaymath}
R = \frac{I_r}{I_i} = \left(\frac{E_r}{E_i}\right)^2.
\end{displaymath}">|; 

$key = q/{displaymath}nabla's=frac{{{bf{r}}{r}-frac{{{bf{u}}{c},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3253.png"
 ALT="\begin{displaymath}
\nabla' s = \frac{{\bf r}}{r} - \frac{{\bf u}}{c},
\end{displaymath}">|; 

$key = q/displaystylea_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle a_{z'}$">|; 

$key = q/lslashv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$l/v$">|; 

$key = q/q,{{bf{v}times{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1784.png"
 ALT="$q  {\bf v}\times {\bf B}$">|; 

$key = q/{{bf{E}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="${\bf E} = {\bf0}$">|; 

$key = q/{displaymath}{calF}_muU^mu=c^2,frac{dm_0}{dtau}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3182.png"
 ALT="\begin{displaymath}
{\cal F}_\mu U^\mu = c^2  \frac{dm_0}{d\tau}.
\end{displaymath}">|; 

$key = q/{displaymath}-A_y(z+dz),dy+A_y(z),dy=-frac{partialA_y}{partialy},dy,dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="\begin{displaymath}
-A_y(z+dz) dy + A_y(z) dy = -\frac{\partial A_y}{\partial y} dy dz.
\end{displaymath}">|; 

$key = q/g_{munu},R^mu,Q^nu=R_mu,Q^mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2899.png"
 ALT="$g_{\mu\nu} R^\mu  Q^\nu = R_\mu  Q^\mu$">|; 

$key = q/displaystylefrac{mu_0,I}{4pi,rho}int_{-pislash2}^{pislash2}cosphi,dphi=frac{mu_0,I}{4pi,rho}left[sinphiright]_{-pislash2}^{pislash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="$\displaystyle \frac{\mu_0  I}{4\pi  \rho} \int_{-\pi/2}^{\pi/2} \cos\phi d\phi
= \frac{\mu_0  I}{4\pi  \rho} \left[ \sin\phi\right]_{-\pi/2}^{\pi/2},$">|; 

$key = q/A_{i'j'k'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2781.png"
 ALT="$A_{i'j'k'}$">|; 

$key = q/displaystyle-frac{partialU}{partialy}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1560.png"
 ALT="$\displaystyle -\frac{\partial U}{\partial y}.$">|; 

$key = q/B=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$B=0.01$">|; 

$key = q/partialB_zslashpartialx=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2610.png"
 ALT="$\partial B_z/\partial x =0$">|; 

$key = q/deltarho_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1753.png"
 ALT="$\delta\rho_f$">|; 

$key = q/{displaymath}p=frac{E}{c}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2144.png"
 ALT="\begin{displaymath}
p = \frac{E}{c}
\end{displaymath}">|; 

$key = q/displaystyleF^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3044.png"
 ALT="$\displaystyle F^{ij}$">|; 

$key = q/phi=phi_{{rm{analogue};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1495.png"
 ALT="$\phi = \phi_{\rm analogue}$">|; 

$key = q/phi_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1397.png"
 ALT="$\phi_S$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$l$">|; 

$key = q/{{bf{a}cdot{{bf{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="${\bf a} \cdot {\bf b}$">|; 

$key = q/displaystyle-G^{ji}=-E^{ij},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3067.png"
 ALT="$\displaystyle -G^{ji} = -E^{ij},$">|; 

$key = q/costhetasimeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\cos\theta\simeq 1$">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig2.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig2.eps}}
\end{figure}">|; 

$key = q/6.8times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1790.png"
 ALT="$6.8\times 10^{-5}$">|; 

$key = q/{displaymath}phi=[,Aexp(k,x)+Bexp(-k,x),],[Csin(k,y)+Dcos(k,y)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1620.png"
 ALT="\begin{displaymath}
\phi = [ A \exp(k x) + B \exp(-k x) ] [C \sin (k y) + D \cos (k y)].
\end{displaymath}">|; 

$key = q/R=Z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2083.png"
 ALT="$R=Z_0$">|; 

$key = q/{displaymath}{{bf{a}times({{bf{b}times{{bf{c})=({{bf{a}cdot{{bf{c}),{{bf{b}-({{bf{a}cdot{{bf{b}),{{bf{c}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="\begin{displaymath}
{\bf a}\times({\bf b}\times{\bf c})= ({\bf a}\cdot{\bf c}) {\bf b} - ({\bf a}\cdot
{\bf b}) {\bf c}
\end{displaymath}">|; 

$key = q/k=omega,[1-(1slash2),omega_p^{,2}slashomega^2]slashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2379.png"
 ALT="$k= \omega [1-(1/2) \omega_p^{ 2}/\omega^2]/c$">|; 

$key = q/{displaymath}frac{E}{B}=c,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="\begin{displaymath}
\frac{E}{B} = c,
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_0,{{rm{e}^{,{{rm{i},({{bf{k}cdot{{bf{r}-omega,t)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2439.png"
 ALT="$\displaystyle {\bf B}_0 {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r}-\omega t)}.$">|; 

$key = q/u_r={{bf{u}!cdot!{{bf{r}_0slashr_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3265.png"
 ALT="$u_r={\bf u}\!\cdot\!{\bf r}_0/r_0$">|; 

$key = q/{figure}{epsfysize{=1.5in{centerline{epsffile{fig44.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="610" HEIGHT="172" BORDER="0"
 SRC="|."$dir".q|img1596.png"
 ALT="\begin{figure}
\epsfysize =1.5in
\centerline{\epsffile{fig44.eps}}
\end{figure}">|; 

$key = q/phi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1494.png"
 ALT="$\phi=0$">|; 

$key = q/int{mitdiv},{{bf{v},,dV=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="$\int {\mit div} {\bf v}  dV = 0$">|; 

$key = q/m_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$m_2$">|; 

$key = q/U_muU^mu=c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3180.png"
 ALT="$U_\mu U^\mu = c^2$">|; 

$key = q/displaystyle{{bf{B}_t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2532.png"
 ALT="$\displaystyle {\bf B}_t$">|; 

$key = q/{x^i}'(t');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3228.png"
 ALT="${x^i}'(t')$">|; 

$key = q/{displaymath}frac{d({A^{icdotsj}}_{kcdotsl})}{ds}={A^{icdotsj}}_{kcdotsl,m}frac{dx^m}{ds},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2851.png"
 ALT="\begin{displaymath}
\frac{d({A^{i\cdots j}}_{k\cdots l})}{ds} = {A^{i\cdots j}}_{k\cdots l,m}
\frac{d x^m}{ds},
\end{displaymath}">|; 

$key = q/{displaymath}G({{bf{r},{{bf{r}';t,t')=-frac{1}{4pi}frac{delta(t-t'-|{{bf{r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="\begin{displaymath}
G({\bf r}, {\bf r}'; t, t') = - \frac{1}{4\pi}
\frac{\delta ...
...\vert{\bf r} - {\bf r}'\vert/c)}{\vert{\bf r}- {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/displaystyle{{bf{B}_0,{{rm{e}^{,{{rm{i},({{bf{k}cdot{{bf{r}-omega,t)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="$\displaystyle {\bf B}_0  {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r} - \omega  t)},$">|; 

$key = q/{displaymath}W=frac{1}{C}int_0^Qq,dq=frac{Q^2}{2,C}=frac{1}{2},C,V^2,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="\begin{displaymath}
W =\frac{1}{C} \int_0^Q q  dq = \frac{Q^2}{2 C} = \frac{1}{2} C V^2,
\end{displaymath}">|; 

$key = q/displaystyleu_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2733.png"
 ALT="$\displaystyle u_3$">|; 

$key = q/{displaymath}G^{4i}=frac{1}{2},epsilon^{4ijk},F_{jk}=-frac{1}{2},epsilon^{ijk4},F_{jk}=frac{1}{2},epsilon^{ijk},c,B_{jk}=c,B^i,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3060.png"
 ALT="\begin{displaymath}
G^{4i} = \frac{1}{2} \epsilon^{4ijk}  F_{jk} = -\frac{1}{2...
...4} F_{jk}
= \frac{1}{2} \epsilon^{ijk}  c B_{jk} = c B^i,
\end{displaymath}">|; 

$key = q/{displaymath}nabla(E^2slash2)equiv{{bf{E}times(nablatimes{{bf{E})+({{bf{E}cdot{nabla}){{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2182.png"
 ALT="\begin{displaymath}
\nabla (E^2/2) \equiv {\bf E}\times(\nabla\times {\bf E}) + ({\bf E}\cdot{\nabla}){\bf E},
\end{displaymath}">|; 

$key = q/{displaymath}{A^i}_j=g^{ip}A_{pj}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2841.png"
 ALT="\begin{displaymath}
{A^i}_j = g^{ip} A_{pj}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{grad},f=nablaf=left(frac{partialf}{partialx},,frac{partialf}{partialy},,frac{partialf}{partialz}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="\begin{displaymath}
{\bf grad} f = \nabla f = \left(\frac{\partial f}{\partial ...
...partial f}{\partial y}, \frac{\partial f}{\partial z}\right).
\end{displaymath}">|; 

$key = q/B_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2597.png"
 ALT="$B_z$">|; 

$key = q/{bf{F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\bf F$">|; 

$key = q/C^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2818.png"
 ALT="$C^{ij}$">|; 

$key = q/dV'=gamma,dV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2993.png"
 ALT="$dV' = \gamma  dV$">|; 

$key = q/{displaymath}int_P^Q{{bf{A}cdotd{{bf{l}=int_P^Q(A_x,dx+A_y,dy+A_z,dz).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="\begin{displaymath}
\int_P^Q {\bf A}\cdot d{\bf l} = \int_P^Q (A_x dx+A_y dy + A_z dz).
\end{displaymath}">|; 

$key = q/{displaymath}{calF}_mu=frac{e}{c},F_{munu},U^nu.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3177.png"
 ALT="\begin{displaymath}
{\cal F}_\mu = \frac{e}{c}  F_{\mu\nu}  U^\nu.
\end{displaymath}">|; 

$key = q/displaystylenablacdot{{bf{E}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1427.png"
 ALT="$\displaystyle \nabla\cdot{\bf E}_2$">|; 

$key = q/displaystyleIrho,,hat{mbox{{boldmath{{theta{}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="$\displaystyle I\rho  \hat{\mbox{\boldmath$\theta$}},$">|; 

$key = q/{displaymath}F=frac{1}{2}({{rm{retarded})+frac{1}{2}({{rm{advanced}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="\begin{displaymath}
F = \frac{1}{2} ({\rm retarded}) + \frac{1}{2} ({\rm advanced}).
\end{displaymath}">|; 

$key = q/{displaymath}langle|{{bf{u}|rangle=c,langleUrangle=1300,{{rm{W,m^{-2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2164.png"
 ALT="\begin{displaymath}
\langle \vert{\bf u}\vert\rangle = c  \langle U\rangle = 1300  {\rm W  m^{-2}},
\end{displaymath}">|; 

$key = q/displaystylenablaU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1565.png"
 ALT="$\displaystyle \nabla U$">|; 

$key = q/{displaymath}(E_i+E_r),frac{sintheta_i}{v_1}=E_t,frac{sintheta_t}{v_2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2536.png"
 ALT="\begin{displaymath}
(E_i + E_r) \frac{\sin\theta_i}{v_1} = E_t \frac{\sin\theta_t}{v_2}.
\end{displaymath}">|; 

$key = q/{displaymath}f_nu=epsilon_0,F_{nusigma},partial_muF^{musigma}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3190.png"
 ALT="\begin{displaymath}
f_\nu = \epsilon_0  F_{\nu\sigma} \partial_\mu F^{\mu\sigma}.
\end{displaymath}">|; 

$key = q/{displaymath}nabla^2T=frac{c}{kappa}frac{partialT}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="\begin{displaymath}
\nabla^2 T = \frac{c}{\kappa} \frac{\partial T}{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=E_0left[{{rm{e}^{,{{rm{i},(k_+,z-omega,t)},{{bf{e}_++{{rm{e}^{,{{rm{i},(k_-,z-omega,t)},{{bf{e}_-right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img2381.png"
 ALT="\begin{displaymath}
{\bf E} = E_0 \left[{\rm e}^{ {\rm i} (k_+ z-\omega t)}\...
...
+ {\rm e}^{ {\rm i} (k_- z-\omega t)} {\bf e}_- \right].
\end{displaymath}">|; 

$key = q/displaystyleE_y(z=0^-).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1703.png"
 ALT="$\displaystyle E_y(z=0^-).$">|; 

$key = q/{displaymath}frac{partial{{bf{g}}{partialt}+nablacdot!{{bf{G}=-rho,{{bf{E}-{{bf{j}times{{bf{B},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3218.png"
 ALT="\begin{displaymath}
\frac{\partial{\bf g}}{\partial t}+\nabla\cdot\!
{\bf G}=
-\rho  {\bf E} - {\bf j}\times{\bf B},
\end{displaymath}">|; 

$key = q/{{bf{E}cdot{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2112.png"
 ALT="${\bf E}\cdot{\bf j}$">|; 

$key = q/displaystylefrac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r'},t-|{{bf{r}-{{bf{r'}|slashc)}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="$\displaystyle \frac{\mu_0}{4\pi } \int \frac{{\bf j}({\bf r'},t- \vert{\bf r}
-{\bf r '}\vert/c
)}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r'}.$">|; 

$key = q/{displaymath}{{bf{j}_perp={{bf{j}-frac{({{bf{j}cdot{{bf{R})}{R^2},{{bf{R}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="\begin{displaymath}
{\bf j}_\perp = {\bf j} - \frac{({\bf j} \cdot {\bf R})}{R^2}  {\bf R}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=frac{q}{4pi,epsilon_0}left(frac{x}{r^3},,,frac{y}{r^3},,,frac{z}{r^3}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="\begin{displaymath}
{\bf E} = \frac{q}{4\pi \epsilon_0} \left(\frac{x}{r^3},   \frac{y}{r^3},
   \frac{z}{r^3}
\right),
\end{displaymath}">|; 

$key = q/{mitDelta}t'={mitDelta}thetaslashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3396.png"
 ALT="${\mit\Delta} t' ={\mit\Delta}\theta/\omega_0$">|; 

$key = q/{displaymath}frac{x-x'}{[(x-x')^2+(y-y')^2+(z-z')^2]^{,3slash2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="\begin{displaymath}
\frac{x - x'}{[(x-x')^2+(y-y')^2 + (z-z')^2]^{ 3/2}}.
\end{displaymath}">|; 

$key = q/I(T)=I_T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1953.png"
 ALT="$I(T) = I_T$">|; 

$key = q/nablatimes(phi,{{bf{A})=phi,nablatimes{{bf{A}+nablaphitimes{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="$\nabla\times(\phi {\bf A})=
\phi \nabla\times{\bf A} + \nabla\phi\times{\bf A}$">|; 

$key = q/xrightarrowpminfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$x\rightarrow\pm\infty$">|; 

$key = q/c_ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="$c_\ast$">|; 

$key = q/{displaymath}(2pi,a-d),H_c+d,H_g=N,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1843.png"
 ALT="\begin{displaymath}
(2\pi a-d) H_c + d H_g = N I.
\end{displaymath}">|; 

$key = q/R_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1918.png"
 ALT="$R_1$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig12.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig12.eps}}
\end{figure}">|; 

$key = q/1slashr^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="$1/r^2$">|; 

$key = q/{{bf{j}=I_i,d{{bf{l}_islashdl_i,A_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1992.png"
 ALT="${\bf j} =I_i  d{\bf l}_i
/dl_i  A_i$">|; 

$key = q/{displaymath}{{bf{B}=frac{mu_0,I}{2pi}left(frac{-y}{r^2},frac{x}{r^2},0right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="\begin{displaymath}
{\bf B} = \frac{\mu_0  I}{2\pi} \left(\frac{-y}{r^2}, \frac{x}{r^2}, 0\right).
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{u}=frac{{{bf{E}times{{bf{B}}{mu_0}=frac{E^2}{mu_0,omega},{{bf{k}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2350.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{{\bf E}\times{\bf B}}{\mu_0} = \frac{E^2}{\mu_0 \omega} {\bf k}.
\end{displaymath}">|; 

$key = q/A=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1621.png"
 ALT="$A=0$">|; 

$key = q/mu=mu_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1797.png"
 ALT="$\mu =\mu_0$">|; 

$key = q/{displaymath}{{bf{f}=frac{d{{bf{p}}{dt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3163.png"
 ALT="\begin{displaymath}
{\bf f} = \frac{d{\bf p}}{dt},
\end{displaymath}">|; 

$key = q/{displaymath}rho_b=-nabla!cdot!{{bf{P}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1674.png"
 ALT="\begin{displaymath}
\rho_b = -\nabla\!\cdot\!{\bf P}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{sigma}{2epsilon_0}mbox{hspace{2cm}above},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="$\displaystyle -\frac{\sigma }{2 \epsilon_0}\mbox{\hspace{2cm} above},$">|; 

$key = q/displaystyle{{bf{A}-nablapsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$\displaystyle {\bf A} - \nabla\psi,$">|; 

$key = q/10^{18};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2166.png"
 ALT="$10^{18}$">|; 

$key = q/{displaymath}r'=-c,t'=-c,gamma,(t-u,xslashc^2)=r,gamma,(1+u_rslashc),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3120.png"
 ALT="\begin{displaymath}
r'=-c t' =-c \gamma (t-u x/c^2) = r \gamma (1+u_r/c),
\end{displaymath}">|; 

$key = q/rho({{bf{r})=q,n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$\rho({\bf r})= q n$">|; 

$key = q/{displaymath}E_{{rm{ext}=frac{sigma}{2,epsilon_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="\begin{displaymath}
E_{\rm ext} = \frac{\sigma}{2 \epsilon_0}
\end{displaymath}">|; 

$key = q/f<100;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2422.png"
 ALT="$f&lt; 100$">|; 

$key = q/displaystyleleftlgrouparray{{cccc}+gamma<col_mark>0<col_mark>0<col_mark>-gamma,b,beta<col_mark>0<col_mark>0<col_mark>+gammaarray{rightrgroup,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="111" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2890.png"
 ALT="$\displaystyle \left\lgroup
\begin{array}{cccc}
+\gamma &amp; 0 &amp; 0 &amp; -\gamma \beta...
...\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
-\gamma \beta &amp; 0 &amp; 0 &amp; +\gamma
\end{array}\right\rgroup,$">|; 

$key = q/displaystyle-frac{mu_0}{4pi}intleft(frac{{{bf{R}times[{{bf{j}]}{R^3}+frac{{{bf{R}times[partial{{bf{j}slashpartialt]}{cR^2}right),dV'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="$\displaystyle -\frac{\mu_0}{4\pi} \int \left( \frac{{\bf R} \times [{\bf j}]}{R^3} +
\frac{{\bf R} \times [\partial {\bf j}/\partial t]}{cR^2} \right) dV'.$">|; 

$key = q/(x^i,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3226.png"
 ALT="$(x^i, t)$">|; 

$key = q/Z_0rightarrowsqrt{Z_0,Z_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2100.png"
 ALT="$Z_0 \rightarrow \sqrt{Z_0  Z_1}$">|; 

$key = q/displaystylel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="$\displaystyle l$">|; 

$key = q/{figure}{epsfysize{=3in{centerline{epsffile{fig5.ps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img1571.png"
 ALT="\begin{figure}
\epsfysize =3in
\centerline{\epsffile{fig5.ps}}
\end{figure}">|; 

$key = q/{displaymath}{mitdiv},({{bf{grad},T)=frac{c}{kappa}frac{partialT}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="\begin{displaymath}
{\mit div} ({\bf grad} T) = \frac{c}{\kappa} \frac{ \partial T}{\partial t}.
\end{displaymath}">|; 

$key = q/m=Eslashc^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2136.png"
 ALT="$m= E/c^2$">|; 

$key = q/k_t=omegaslashv_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2511.png"
 ALT="$k_t=\omega/v_2$">|; 

$key = q/{displaymath}{{bf{f}({{bf{r})=qsum_{i=1}^Nfrac{q_i}{4pi,epsilon_0}frac{{{bf{r}-{{bf{r}_i}{|{{bf{r}-{{bf{r}_i|^3}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="\begin{displaymath}
{\bf f}({\bf r}) = q \sum_{i=1}^N \frac{q_i}{4\pi \epsilon_0}
\frac{{\bf r}-{\bf r}_i}{\vert{\bf r}-{\bf r}_i\vert^3}.
\end{displaymath}">|; 

$key = q/|A|=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="$\vert A\vert = 1$">|; 

$key = q/{displaymath}A_{k'cdotsl'}^{i'cdotsj'}=A_{kcdotsl}^{icdotsj},p_i^{i'}cdotsp_j^{j'},p^k_{k'}cdotsp^{l}_{l'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2798.png"
 ALT="\begin{displaymath}
A_{k'\cdots l'}^{i'\cdots j'} = A_{k\cdots l}^{i\cdots j} 
p_i^{i'} \cdots p_j^{j'}  p^k_{k'}\cdots p^{l}_{l'}.
\end{displaymath}">|; 

$key = q/{displaymath}int{{bf{E}'!cdot!(nablatimes{{bf{H}),d^3{{bf{r}=intfrac{(nablatimes-int{{bf{E}!cdot!(nablatimes{{bf{H}),d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1849.png"
 ALT="\begin{displaymath}
\int {\bf E}'\!\cdot\!(\nabla\times{\bf H}) d^3{\bf r}
= \i...
... r} - \int {\bf E}\!\cdot\!(\nabla\times{\bf H}) 
d^3{\bf r}.
\end{displaymath}">|; 

$key = q/displaystyle{{rm{i},omega,B_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2581.png"
 ALT="$\displaystyle {\rm i} \omega B_z$">|; 

$key = q/v_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$v_\parallel$">|; 

$key = q/m,n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2618.png"
 ALT="$m, n$">|; 

$key = q/{displaymath}frac{partialrho}{partialt}+nablacdot{{bf{j}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2107.png"
 ALT="\begin{displaymath}
\frac{\partial\rho}{\partial t} +\nabla\cdot {\bf j} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}A^{i'j'cdotsk'}=A^{ijcdotsk}p_i^{i'},p_j^{j'}cdotsp_k^{k'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img2794.png"
 ALT="\begin{displaymath}
A^{i'j'\cdots k'} = A^{ij\cdots k} p_i^{i'}  p_j^{j'} \cdots p_k^{k'}.
\end{displaymath}">|; 

$key = q/{displaymath}phi=V_0,left(frac{x}{d}right)^{4slash3},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1483.png"
 ALT="\begin{displaymath}
\phi = V_0 \left(\frac{x}{d}\right)^{4/3},
\end{displaymath}">|; 

$key = q/S_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$S_1$">|; 

$key = q/vllc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2721.png"
 ALT="$v \ll c$">|; 

$key = q/rho_f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1675.png"
 ALT="$\rho_f$">|; 

$key = q/{{bf{b}=(b_x,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="${\bf b} = (b_x, 0, 0)$">|; 

$key = q/{displaymath}{{bf{a}times{{bf{b}=-{{bf{b}times{{bf{a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="\begin{displaymath}
{\bf a}\times{\bf b} = - {\bf b} \times{\bf a},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{M}({{bf{r})=sum_iN_ilangle{{bf{m}_irangle,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1769.png"
 ALT="\begin{displaymath}
{\bf M} ({\bf r}) = \sum_i N_i \langle {\bf m}_i\rangle,
\end{displaymath}">|; 

$key = q/m_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$m_1$">|; 

$key = q/displaystyle4pitimes10^{-7},{{rm{N},{{rm{A}^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$\displaystyle 4\pi\times 10^{-7} {\rm N}  {\rm A}^{-2}.$">|; 

$key = q/{displaymath}nablacdot{{bf{W}=frac{1}{4pi}intfrac{nabla'!cdot!{{bf{C}({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf W} = \frac{1}{4\pi}\int \frac{\nabla'\!\cdot...
...bf C}({\bf r}') }
{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r'}
\end{displaymath}">|; 

$key = q/{displaymath}U=frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2106.png"
 ALT="\begin{displaymath}
U= \frac{\epsilon_0 E^2}{2}+\frac{B^2}{2 \mu_0}.
\end{displaymath}">|; 

$key = q/{displaymath}frac{q+q'}{epsilon_1}=frac{q''}{epsilon_2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1715.png"
 ALT="\begin{displaymath}
\frac{q+q'}{\epsilon_1} = \frac{q''}{\epsilon_2},
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{2}left(sqrt{L_1},I_1+sqrt{L_2},I_2right)^2-I_1,I_2(sqrt{L_1,L_2}-M)geq0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="393" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1967.png"
 ALT="\begin{displaymath}
\frac{1}{2}\left( \sqrt{L_1}  I_1 + \sqrt{L_2} I_2\right)^2 - I_1  I_2 (\sqrt{L_1  L_2}
-M) \geq 0,
\end{displaymath}">|; 

$key = q/displaystyleF_z[,k,(r-c,t),].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="$\displaystyle F_z [ k (r-c t) ].$">|; 

$key = q/delta{{bf{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="$\delta
{\bf r}$">|; 

$key = q/1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2155.png"
 ALT="$1/2$">|; 

$key = q/sinthetasimeqtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\sin\theta \simeq \theta$">|; 

$key = q/{displaymath}nablacdot{{bf{W}=frac{1}{4pi}int{{bf{C}({{bf{r'})cdotnablaleft(fract(frac{1}{|{{bf{r}-{{bf{r}'|}right),d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="589" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="\begin{displaymath}
\nabla\cdot{\bf W} = \frac{1}{4\pi} \int {\bf C}({\bf r'})\c...
...t( \frac{1}{\vert{\bf r} - {\bf r}'\vert}\right) d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/displaystylenabla^2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$\displaystyle \nabla^2 \phi$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{1}{4piepsilon_0}intfrac{rho({{bf{r}',t)}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="\begin{displaymath}
\phi({\bf r},t)= \frac{1}{4\pi\epsilon_0}
\int \frac{\rho({\bf r}',t)}{\vert{\bf r} - {\bf r}'\vert}  d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{{bf{a}cdot{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="${\bf a} \cdot {\bf a}$">|; 

$key = q/dW=V,dq=q,dqslashC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$dW= V dq = q dq/C$">|; 

$key = q/dh;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$dh$">|; 

$key = q/{displaymath}{T^mu}_nu=epsilon_0left[F^{musigma}F_{sigmanu}+frac{1}{4},delta_nu^mu,(F^{rhosigma}F_{rhosigma})right]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3196.png"
 ALT="\begin{displaymath}
{T^\mu}_\nu = \epsilon_0\left[ F^{\mu\sigma}F_{\sigma\nu}
+ ...
...1}{4}  \delta_\nu^\mu  (F^{\rho\sigma}F_{\rho\sigma})\right]
\end{displaymath}">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=frac{dphi}{dt},{{bf{b}+phi,frac{d{{bf{b}}{dt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \frac{d\phi}{dt}  {\bf b} + \phi  \frac{d {\bf b}}{dt}.
\end{displaymath}">|; 

$key = q/g,frightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="$g f\rightarrow 0$">|; 

$key = q/displaystyle-F_{ji}=-c,B_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3037.png"
 ALT="$\displaystyle -F_{ji} = -c B_{ij}.$">|; 

$key = q/partialTslashpartialt<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\partial T/\partial t&lt;0$">|; 

$key = q/{displaymath}{{bf{p}(t)=p_0,sin(omega,t),hat{{bf{z},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2263.png"
 ALT="\begin{displaymath}
{\bf p}(t) = p_0 \sin(\omega t) \hat{\bf z},
\end{displaymath}">|; 

$key = q/displaystylegamma,(T^1-beta,T^4),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2881.png"
 ALT="$\displaystyle \gamma (T^1-\beta  T^4),$">|; 

$key = q/{displaymath}frac{partial|{{bf{r}-{{bf{r}'|}{partialx}=frac{x-x'}{|{{bf{r}-{{bf{r}'|}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="\begin{displaymath}
\frac{\partial \vert{\bf r} - {\bf r}'\vert}{\partial x} = \frac{x-x'}{\vert{\bf r} - {\bf r}'\vert}.
\end{displaymath}">|; 

$key = q/{mitDelta}E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3390.png"
 ALT="${\mit\Delta} E$">|; 

$key = q/{displaymath}{mitPhi}_i={mitPhi}_{0,i},frac{t}{T}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1985.png"
 ALT="\begin{displaymath}
{\mit\Phi}_i = {\mit\Phi}_{0 i}  \frac{t}{T}.
\end{displaymath}">|; 

$key = q/{displaymath}intdelta({{bf{r}),d^3{{bf{r}=int_{-a}^{a}delta(x),dxint_{-a}^{a}delta(y),dyint_{-a}^{a}delta(z),dz.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="376" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="\begin{displaymath}
\int \delta({\bf r}) d^3{\bf r} = \int_{-a}^{a} \delta(x) dx
\int_{-a}^{a} \delta(y) dy \int_{-a}^{a} \delta(z) dz.
\end{displaymath}">|; 

$key = q/B_{x,1}=B_{x,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2537.png"
 ALT="$B_{x 1} = B_{x 2}$">|; 

$key = q/{displaymath}{{bf{P}=frac{n,e^2}{m_e,(omega_0^{,2}-omega^2)},{{bf{E}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2321.png"
 ALT="\begin{displaymath}
{\bf P} = \frac{n e^2}{m_e (\omega_0^{ 2}-\omega^2)} {\bf E}.
\end{displaymath}">|; 

$key = q/{displaymath}p_0=frac{e^2,E_0}{m_e,(omega^2-omega_0^{,2})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2302.png"
 ALT="\begin{displaymath}
p_0 = \frac{e^2 E_0}{m_e (\omega^2-\omega_0^{ 2})}.
\end{displaymath}">|; 

$key = q/{displaymath}langlePrangle=frac{1}{2},{{rm{Re}(sigma),E_0^{,2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2431.png"
 ALT="\begin{displaymath}
\langle P\rangle = \frac{1}{2}  {\rm Re}(\sigma) E_0^{ 2},
\end{displaymath}">|; 

$key = q/displaystyleleft(frac{partial^2}{partialx^2}+frac{partial^2}{partialy^2}right)!E_z+left(frac{omega^2}{c^2}-k^2right)!E_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2598.png"
 ALT="$\displaystyle \left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}\right)\!
E_z + \left(\frac{\omega^2}{c^2}-k^2\right)\!E_z$">|; 

$key = q/displaystyleoint_{S_i}{{bf{E}_2cdotd{{bf{S}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1431.png"
 ALT="$\displaystyle \oint_{S_i} {\bf E}_2\cdot d{\bf S}_i$">|; 

$key = q/{displaymath}{mitPhi}^mu=(c,{{bf{A},phi){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2974.png"
 ALT="\begin{displaymath}
{\mit \Phi}^\mu = (c {\bf A}, \phi)
\end{displaymath}">|; 

$key = q/omegallnu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2434.png"
 ALT="$\omega\ll\nu$">|; 

$key = q/{displaymath}frac{P}{m_0,c^2}=frac{2}{3}frac{omega_0^{,2},r_0}{c},beta^2,gamma^4,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img3385.png"
 ALT="\begin{displaymath}
\frac{P}{m_0 c^2} = \frac{2}{3} \frac{\omega_0^{ 2}  r_0}{c}  \beta^2 \gamma^4,
\end{displaymath}">|; 

$key = q/displaystylenablatimes{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$\displaystyle \nabla\times{\bf B}$">|; 

$key = q/{displaymath}{{bf{k}cdot{{bf{r}=omega,t+n,2pi+phi,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="\begin{displaymath}
{\bf k}\cdot {\bf r} = \omega  t + n 2\pi+\phi,
\end{displaymath}">|; 

$key = q/{displaymath}nablacdot{{bf{B}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="\begin{displaymath}
\nabla \cdot {\bf B} = 0.
\end{displaymath}">|; 

$key = q/{figure}{epsfysize{=2.5in{centerline{epsffile{fig41.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="\begin{figure}
\epsfysize =2.5in
\centerline{\epsffile{fig41.eps}}
\end{figure}">|; 

$key = q/x=v,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2707.png"
 ALT="$x=v t$">|; 

$key = q/dV=r^2,sintheta,dr,dtheta,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$dV = r^2 \sin\theta dr d\theta d\phi$">|; 

$key = q/r^2=x^2+y^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1503.png"
 ALT="$r^2 = x^2+y^2$">|; 

$key = q/{{bf{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="${\bf D}$">|; 

$key = q/{displaymath}nablacdotnablatimes{{bf{A}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="\begin{displaymath}
\nabla\cdot\nabla \times {\bf A} = 0
\end{displaymath}">|; 

$key = q/{displaymath}J_m=frac{B_{parallel,2}-B_{parallel,1}}{mu_0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1812.png"
 ALT="\begin{displaymath}
J_m= \frac{B_{\parallel 2}-B_{\parallel 1}}{\mu_0}.
\end{displaymath}">|; 

$key = q/displaystyleF(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1536.png"
 ALT="$\displaystyle F(z)$">|; 

$key = q/{displaymath}G=6.6726times10^{-11},,{{rm{N,m^2,kg^{-2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="\begin{displaymath}
G = 6.6726\times 10^{-11}  {\rm N  m^2  kg^{-2}}.
\end{displaymath}">|; 

$key = q/|{{bf{C}({{bf{r})|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$\vert{\bf C}({\bf r})\vert$">|; 

$key = q/displaystyleint_0^adrint_0^{pislash2}dthetaint_0^{2pi}dphi,,r,costheta,,r^2sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$\displaystyle \int_0^a dr\int_0^{\pi/2} d\theta \int_0^{2\pi} d\phi  r \cos\theta 
 
r^2 \sin\theta$">|; 

$key = q/{displaymath}frac{1}{2}(V,I^ast+V^ast,I)=|V_0|,|I_0|,costheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img2025.png"
 ALT="\begin{displaymath}
\frac{1}{2} ( V  I^\ast +V^\ast  I)=
\vert V_0\vert  \vert I_0\vert  \cos\theta.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=-nablaphi=-nablaV={{bf{0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1421.png"
 ALT="\begin{displaymath}
{\bf E} = - \nabla\phi = -\nabla V = {\bf0}
\end{displaymath}">|; 

$key = q/displaystyley',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2723.png"
 ALT="$\displaystyle y',$">|; 

$key = q/displaystylev_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="$\displaystyle v_y$">|; 

$key = q/{displaymath}W=frac{3}{5}frac{Q^2}{4pi,epsilon_0,a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="\begin{displaymath}
W = \frac{3}{5} \frac{Q^2}{4\pi \epsilon_0  a}.
\end{displaymath}">|; 

$key = q/displaystyley';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle y'$">|; 

$key = q/{displaymath}V=L,frac{dI}{dt}+R,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1942.png"
 ALT="\begin{displaymath}
V = L \frac{d I}{dt} + R I.
\end{displaymath}">|; 

$key = q/x^sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2918.png"
 ALT="$x^\sigma$">|; 

$key = q/{displaymath}{mitPhi}^murightarrow{mitPhi}^mu+c,partial^mupsi.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2979.png"
 ALT="\begin{displaymath}
{\mit \Phi}^\mu \rightarrow {\mit \Phi}^\mu + c \partial^\mu \psi.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{u}=frac{|E|^2}{mu_0,omega},{{rm{Re}({{bf{k}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2351.png"
 ALT="\begin{displaymath}
{\bf u} = \frac{\vert E\vert^2}{\mu_0 \omega} {\rm Re}({\bf k}).
\end{displaymath}">|; 

$key = q/displaystyle(a_y,c_y,b_x,,-a_x,b_x,c_y,,0)={{rm{LHS},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle (a_y  c_y  b_x,  -a_x  b_x  c_y,  0 ) = {\rm LHS},$">|; 

$key = q/{displaymath}int_Snablatimes{{bf{B}cdotd{{bf{S}=mu_0,Iint_{-infty}^inftydelta(x),dxint_{-infty}^{infty}delta(y),dy=mu_0,I,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="\begin{displaymath}
\int_S \nabla\times{\bf B} \cdot d{\bf S} = \mu_0  I \int_{...
...elta(x)  dx\int_{-\infty}^{\infty}
\delta(y) dy = \mu_0  I,
\end{displaymath}">|; 

$key = q/{displaymath}{{rm{Rate~of~flow}={{bf{v}cdot{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="\begin{displaymath}
{\rm Rate&nbsp;of&nbsp;flow} = {\bf v}\cdot{\bf S}.
\end{displaymath}">|; 

$key = q/C_k=A^{ij}B_{ijk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2812.png"
 ALT="$C_k = A^{ij} B_{ijk}$">|; 

$key = q/T^{munu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3205.png"
 ALT="$T^{\mu\nu}$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}times{{bf{c}={{bf{a}times{{bf{b}cdot{{bf{c}={{bf{f{c}times{{bf{a}=-{{bf{b}cdot{{bf{a}times{{bf{c}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="\begin{displaymath}
{\bf a}\cdot {\bf b}\times{\bf c} = {\bf a}\times{\bf b}\cdo...
...}\cdot{\bf c}\times{\bf a} = -{\bf b}\cdot{\bf a}\times{\bf c}
\end{displaymath}">|; 

$key = q/displaystyle(a_y,b_z-a_z,b_y),costheta+(a_z,b_x-a_x,b_z),sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle (a_y  b_z - a_z  b_y)  \cos\theta + (a_z  b_x-a_x  b_z) \sin\theta$">|; 

$key = q/{displaymath}frac{|t-t_r|}{t_0}=frac{R}{R_0}ll1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="\begin{displaymath}
\frac{\vert t -t_r\vert}{t_0} = \frac{R}{R_0} \ll 1,
\end{displaymath}">|; 

$key = q/u'=({u'_1}^{2}+{u'_2}^{2}+{u'_3}^{2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2757.png"
 ALT="$u'=({u'_1}^{2} + {u'_2}^{2}+ {u'_3}^{2})^{1/2}$">|; 

$key = q/displaystylet.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2658.png"
 ALT="$\displaystyle t.$">|; 

$key = q/f=m_0,a_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3156.png"
 ALT="$f=m_0  a_0$">|; 

$key = q/B=mu_0,I_1slash2pi,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$B = \mu_0  I_1/2\pi  r$">|; 

$key = q/phi(k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2340.png"
 ALT="$\phi(k)$">|; 

$key = q/{displaymath}rho=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="\begin{displaymath}
\rho = 0.
\end{displaymath}">|; 

$key = q/{displaymath}W=int_P^Q{{bf{f}cdotd{{bf{l},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="\begin{displaymath}
W = \int_P^Q {\bf f}\cdot d{\bf l},
\end{displaymath}">|; 

$key = q/a_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$a_y$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}times{{bf{c}={{bf{b}cdot{{bf{c}times{{bf{a}={{bf{c}cdot{{bf{a}times{{bf{b},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b} \times{\bf c} = {\bf b} \cdot {\bf c} \times{\bf a} =
{\bf c} \cdot {\bf a} \times{\bf b},
\end{displaymath}">|; 

$key = q/displaystyleB_parallel';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3095.png"
 ALT="$\displaystyle B_\parallel'$">|; 

$key = q/displaystylec,A_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3109.png"
 ALT="$\displaystyle c A_1$">|; 

$key = q/displaystyle+frac{sigma}{2epsilon_0}mbox{hspace{2cm}above},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$\displaystyle +\frac{\sigma }{2 \epsilon_0}\mbox{\hspace{2cm} above},$">|; 

$key = q/{displaymath}{{bf{grad},h=left(frac{partialh}{partialx},,frac{partialh}{partialy}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="\begin{displaymath}
{\bf grad} h = \left(\frac{\partial h}{\partial x},  \frac{\partial h}{\partial y}
\right).
\end{displaymath}">|; 

$key = q/{displaymath}oint_C{{bf{B}cdotd{{bf{l}=ointB_theta,r,dtheta=mu_0,I.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="\begin{displaymath}
\oint_C {\bf B} \cdot d{\bf l} = \oint B_\theta  r d\theta= \mu_0  I.
\end{displaymath}">|; 

$key = q/nablatimes{{bf{B}=mu_0,{{bf{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="$\nabla\times{\bf B} = \mu_0  {\bf j}$">|; 

$key = q/lambdasim2000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2421.png"
 ALT="$\lambda\sim 2000$">|; 

$key = q/A_{ijk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2772.png"
 ALT="$A_{ijk}$">|; 

$key = q/{displaymath}int_P^Q=int_{0}^1left[y^3,dy+(y+1),dyright]=frac{7}{4}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="\begin{displaymath}
\int_P^Q = \int_{0}^1\left[y^3 dy + (y+1) dy\right] = \frac{7}{4}.
\end{displaymath}">|; 

$key = q/{displaymath}{calF}_mu=frac{d(m_0,U_mu)}{dtau}=m_0,A_mu+frac{dm_0}{dtau},U_mu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img3179.png"
 ALT="\begin{displaymath}
{\cal F}_\mu =\frac{d(m_0  U_\mu)}{d\tau} = m_0  A_\mu + \frac{dm_0}{d\tau}
 U_\mu,
\end{displaymath}">|; 

$key = q/displaystylefrac{partial^2V}{partialx^2}+frac{partial^2V}{partialy^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1564.png"
 ALT="$\displaystyle \frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2}$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig11.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig11.eps}}
\end{figure}">|; 

$key = q/{displaymath}U=frac{epsilon_0,E^2}{2}+frac{B^2}{2,mu_0}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2124.png"
 ALT="\begin{displaymath}
U = \frac{\epsilon_0 E^2}{2} + \frac{B^2}{2 \mu_0}
\end{displaymath}">|; 

$key = q/mu_0,N_1,I_1,pi,r^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1908.png"
 ALT="$\mu_0  N_1  I_1 \pi  r^2$">|; 

$key = q/displaystylefrac{1}{4pi,epsilon_0}intfrac{left[rho({{bf{r}')right]}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="$\displaystyle \frac{1}{4\pi  \epsilon_0} \int
\frac{\left[\rho({\bf r}')\right]}{\vert{\bf r} - {\bf r}'\vert} d^3{\bf r'},$">|; 

$key = q/displaystyle-mu_0,j_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$\displaystyle - \mu_0  j_x,$">|; 

$key = q/displaystyleBoxphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2970.png"
 ALT="$\displaystyle \Box \phi$">|; 

$key = q/{displaymath}{mitdiv},{{bf{A}=frac{partialA_x}{partialx}+frac{partialA_y}{partialy}+frac{partialA_z}{partialz},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="\begin{displaymath}
{\mit div} {\bf A} = \frac{\partial A_x}{\partial x} +
\frac{\partial A_y}{\partial y} +\frac{\partial A_z}{\partial z},
\end{displaymath}">|; 

$key = q/c,B_{ij}rightarrowE_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3081.png"
 ALT="$c B_{ij} \rightarrow E_{ij}$">|; 

$key = q/displaystylenablacdot{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="$\displaystyle \nabla\cdot {\bf A}$">|; 

$key = q/displaystyleE_i,hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2523.png"
 ALT="$\displaystyle E_i \hat{\bf y},$">|; 

$key = q/N(x,y,z),q,d_x,dy,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1667.png"
 ALT="$N(x,y,z) q d_x dy dz$">|; 

$key = q/{displaymath}Z_{{rm{in}=frac{V(0,t)}{I(0,t)}=sqrt{frac{L}{C}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img2063.png"
 ALT="\begin{displaymath}
Z_{\rm in} = \frac{V(0, t)}{I(0, t)} = \sqrt{\frac{L}{C}}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{partial{{bf{B}}{partialt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3083.png"
 ALT="$\displaystyle -\frac{\partial{\bf B}}{\partial t}.$">|; 

$key = q/{displaymath}nabla({{bf{A}cdot{{bf{B})={{bf{A}times(nablatimes{{bf{B})+{{bf{B}tibf{A}cdotnabla){{bf{B}+({{bf{B}cdotnabla){{bf{A}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="537" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="\begin{displaymath}
\nabla({\bf A}\cdot{\bf B}) = {\bf A}\times(\nabla\times{\bf...
... +({\bf A}\cdot \nabla){\bf B} + ({\bf B} \cdot
\nabla){\bf A}
\end{displaymath}">|; 

$key = q/(x^1,x^2,cdots,x^n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2777.png"
 ALT="$(x^1, x^2, \cdots, x^n)$">|; 

$key = q/{displaymath}{{bf{E}=E_+,{{rm{e}^{,{{rm{i},(k_+,z-omega,t)},{{bf{e}_++E_-,{{rm{e}^{,{{rm{i},(k_-,z-omega,t)},{{bf{e}_-.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2369.png"
 ALT="\begin{displaymath}
{\bf E} = E_+ {\rm e}^{ {\rm i} (k_+ z-\omega t)} {\bf e}_+
+ E_- {\rm e}^{ {\rm i} (k_- z-\omega t)} {\bf e}_-.
\end{displaymath}">|; 

$key = q/oint_S{{bf{B}cdotd{{bf{S}neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$\oint_S {\bf B}\cdot d{\bf S} \neq 0$">|; 

$key = q/{displaymath}E_x=-frac{partialphi}{partialx}=-{calV},frac{partialU}{partialx}=-2,{calV},x{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1578.png"
 ALT="\begin{displaymath}
E_x = - \frac{\partial\phi}{\partial x} =- {\cal V}  \frac{\partial U}{\partial x}
= -2  {\cal V}  x
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{A}={{bf{A}_0,{{rm{e}^{,{{rm{i},({{bf{k}cdot{{bf{r}-omega,t)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="\begin{displaymath}
{\bf A} = {\bf A}_0  {\rm e}^{ {\rm i} ({\bf k}\cdot{\bf r} - \omega  t)}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{A}({{bf{r})=frac{mu_0}{4pi}intfrac{{{bf{j}({{bf{r}')}{|{{bf{r}-{{bf{r}'|},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="\begin{displaymath}
{\bf A}({\bf r}) = \frac{\mu_0}{4\pi}
\int \frac{{\bf j}({\bf r}')}{\vert{\bf r} - {\bf r}'\vert}
 d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/F_z(phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="$F_z(\phi)$">|; 

$key = q/{displaymath}(nablatimes{{bf{A})^i=epsilon^{ijk},frac{partialA_k}{partialx^j}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img3005.png"
 ALT="\begin{displaymath}
(\nabla\times{\bf A})^i = \epsilon^{ijk}  \frac{\partial A_k}{\partial x^j}.
\end{displaymath}">|; 

$key = q/x^irightarrowx^{i'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2791.png"
 ALT="$x^i\rightarrow x^{i'}$">|; 

$key = q/E=m,c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2137.png"
 ALT="$E=m  c^2$">|; 

$key = q/{displaymath}dE^{'}=gamma(u)left(dE+u,dp^1right)=gamma,dE.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img3313.png"
 ALT="\begin{displaymath}
dE^{'} = \gamma(u) \left(dE + u dp^1\right) = \gamma  dE.
\end{displaymath}">|; 

$key = q/100%;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2571.png"
 ALT="$100\%$">|; 

$key = q/{{bf{u}^i=cT^{i4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3215.png"
 ALT="${\bf u}^i = c T^{i4}$">|; 

$key = q/{displaymath}{{bf{a}cdot{{bf{b}times{{bf{c}={{bf{a}times{{bf{b}cdot{{bf{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="\begin{displaymath}
{\bf a} \cdot {\bf b}\times{\bf c} = {\bf a} \times{\bf b} \cdot{\bf c}.
\end{displaymath}">|; 

$key = q/nu^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2426.png"
 ALT="$\nu^{-1}$">|; 

$key = q/{displaymath}Deltat'=gamma,(Deltat-v,Deltaxslashc^2)=gamma,Deltat,(1-v,Uslashc^2).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2767.png"
 ALT="\begin{displaymath}
\Delta t' = \gamma (\Delta t - v \Delta x/c^2) = \gamma \Delta t 
(1-v  U/c^2).
\end{displaymath}">|; 

$key = q/(dhslashdl)_{{rm{max};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$(dh/dl)_{\rm max}$">|; 

$key = q/k_1=omegaslashv_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2454.png"
 ALT="$k_1=\omega/v_1$">|; 

$key = q/displaystylenablacdot{{bf{F}=D,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="$\displaystyle \nabla\cdot {\bf F} = D,$">|; 

$key = q/10^9,{{rm{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2295.png"
 ALT="$10^9 {\rm m}$">|; 

$key = q/{displaymath}h_T(x,,y)=h(x_0,,y_0)+alpha,(x-x_0)+beta,(y-y_0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="\begin{displaymath}
h_T(x, y)= h(x_0, y_0) + \alpha (x-x_0)+\beta (y-y_0).
\end{displaymath}">|; 

$key = q/{displaymath}sigma=ointfrac{dsigma}{d{mitOmega}},d{mitOmega},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2283.png"
 ALT="\begin{displaymath}
\sigma = \oint \frac{d\sigma}{d{\mit\Omega}} d{\mit\Omega},
\end{displaymath}">|; 

$key = q/displaystylefrac{rho,c}{c,epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2971.png"
 ALT="$\displaystyle \frac{\rho  c}{c \epsilon_0},$">|; 

$key = q/V_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1927.png"
 ALT="$V_2$">|; 

$key = q/lambda=0.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="$\lambda= 0.4$">|; 

$key = q/displaystyle|a|^2,|b|^2-|a|^2,|b|^2,cos^2theta=|a|^2,|b|^2,sin^2theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle \vert a\vert^2  \vert b\vert^2 - \vert a\vert^2  \vert b\vert^2  \cos^2\theta = \vert a\vert^2 \vert b\vert^2  \sin^2\theta.$">|; 

$key = q/{displaymath}E_z=eta,j_z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="\begin{displaymath}
E_z = \eta  j_z.
\end{displaymath}">|; 

$key = q/E_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3055.png"
 ALT="$E_{ij}$">|; 

$key = q/{{bf{a}times({{bf{b}times{{bf{c})neq({{bf{a}times{{bf{b})times{{bf{c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="${\bf a}\times({\bf b} \times {\bf c}) \neq ({\bf a}\times{\bf b} )\times {\bf c}$">|; 

$key = q/({{bf{curl},{{bf{v})_z=2,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$({\bf curl} {\bf v})_z = 2 \omega$">|; 

$key = q/displaystylea_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle a_z,$">|; 

$key = q/{displaymath}nablatimes{{bf{E}=-frac{partial{{bf{B}}{partialt}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2441.png"
 ALT="\begin{displaymath}
\nabla\times {\bf E} = -\frac{\partial {\bf B}}{\partial t}
\end{displaymath}">|; 

$key = q/{displaymath}F^{musigma},partial_muF_{nusigma}=frac{1}{2},F^{musigma}(partial_muF_{nusigma}+partial_sigmaF_{munu}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img3192.png"
 ALT="\begin{displaymath}
F^{\mu\sigma}  \partial_\mu F_{\nu\sigma} = \frac{1}{2}  F...
...ma}
(\partial_\mu F_{\nu\sigma} + \partial_\sigma F_{\mu\nu}),
\end{displaymath}">|; 

$key = q/{displaymath}-epsilon_0,frac{partial{{bf{E}}{partialt}times{{bf{B}=frac{{{bf{B}ts(nablatimes{{bf{B})}{mu_0}+{{bf{j}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2177.png"
 ALT="\begin{displaymath}
-\epsilon_0 \frac{\partial {\bf E}}{\partial t}\times {\bf ...
...}\times(\nabla\times {\bf B})}{\mu_0} + {\bf j}\times {\bf B}.
\end{displaymath}">|; 

$key = q/d{{bf{S}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1864.png"
 ALT="$d{\bf S}_2$">|; 

$key = q/displaystylemu_0int_S{{bf{j}cdotd{{bf{S}+frac{1}{c^2}frac{partial}{partialt}!int_S{{bf{E}cdotd{{bf{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="$\displaystyle \mu_0\int_S {\bf j}\cdot
d{\bf S} + \frac{1}{c^2}\frac{\partial }{\partial t}\!\int_S {\bf E} \cdot d{\bf S}.$">|; 

$key = q/{displaymath}u({{bf{r})=intG({{bf{r},{{bf{r}'),v({{bf{r}'),d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="\begin{displaymath}
u({\bf r}) = \int G({\bf r}, {\bf r}')  v({\bf r}') d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{displaymath}v=frac{1}{sqrt{L,C}}=frac{1}{sqrt{epsilon_0,mu_0}}=c.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2070.png"
 ALT="\begin{displaymath}
v = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{\epsilon_0  \mu_0}} = c.
\end{displaymath}">|; 

$key = q/B^1=B_1equivB_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3020.png"
 ALT="$B^1=B_1 \equiv B_x$">|; 

$key = q/C_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1629.png"
 ALT="$C_n$">|; 

$key = q/{{bf{W}rightarrow{{bf{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="${\bf W}\rightarrow{\bf A}$">|; 

$key = q/displaystylefrac{n,pi}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2613.png"
 ALT="$\displaystyle \frac{n \pi}{a},$">|; 

$key = q/{displaymath}{{bf{grad},phi=left(frac{partialphi}{partialx},,frac{partialphi}{partialy},,frac{partialphi}{partialz}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="\begin{displaymath}
{\bf grad} \phi = \left(\frac{\partial \phi}{\partial x}, ...
... \phi}
{\partial y}, 
\frac{\partial \phi}{\partial z}\right)
\end{displaymath}">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="$v$">|; 

$key = q/10^9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$10^9$">|; 

$key = q/g_{mu'nu'},dx^{mu'},dx^{nu'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2916.png"
 ALT="$g_{\mu'\nu'}  dx^{\mu'}  dx^{\nu'}$">|; 

$key = q/displaystylefrac{dv_z}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="$\displaystyle \frac{d v_z}{dt}$">|; 

$key = q/displaystylefrac{partialB_z}{partialy}-frac{partialB_y}{partialz}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="$\displaystyle \frac{\partial B_z}{\partial y} - \frac{\partial B_y}
{\partial z} = 0,$">|; 

$key = q/{displaymath}B^mu=intQ^{4mu},d^3x.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img3302.png"
 ALT="\begin{displaymath}
B^\mu = \int Q^{4\mu} d^3 x.
\end{displaymath}">|; 

$key = q/{displaymath}W=frac{1}{2}int{{bf{H}!cdot!{{bf{B},d^3{{bf{r}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1858.png"
 ALT="\begin{displaymath}
W = \frac{1}{2} \int {\bf H}\!\cdot\!{\bf B}  d^3{\bf r}.
\end{displaymath}">|; 

$key = q/A^mu=(dot{{bf{u},0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3317.png"
 ALT="$A^\mu =
(\dot{\bf u}, 0)$">|; 

$key = q/{displaymath}z=x+{{rm{i},y{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1534.png"
 ALT="\begin{displaymath}
z = x + {\rm i} y
\end{displaymath}">|; 

$key = q/{displaymath}[rho({{bf{r},t)]simeqrho({{bf{r},t-R_astslashc),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="\begin{displaymath}[ \rho({\bf r}, t)]\simeq \rho({\bf r}, t - R_\ast/c),
\end{displaymath}">|; 

$key = q/Esim10^8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="$E\sim 10^8$">|; 

$key = q/textstylerightarrow;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="$\textstyle \rightarrow$">|; 

$key = q/R_ast=|{{bf{r}-{{bf{r}_ast|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="$R_\ast
= \vert{\bf r} - {\bf r}_\ast\vert$">|; 

$key = q/{displaymath}sin(k,pi)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1624.png"
 ALT="\begin{displaymath}
\sin (k  \pi) = 0,
\end{displaymath}">|; 

$key = q/{{bf{B}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="${\bf B}_2$">|; 

$key = q/displaystyleE_t,(costheta_t,,0,,-sintheta_t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2550.png"
 ALT="$\displaystyle E_t (\cos\theta_t,  0, -\sin\theta_t),$">|; 

$key = q/{displaymath}nablacdot{{bf{E}=sum_{i=1}^Nfrac{q_i}{epsilon_0},delta({{bf{r}-{{bf{r}_i).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="\begin{displaymath}
\nabla\cdot {\bf E} = \sum_{i=1}^N
\frac{q_i}{\epsilon_0}  \delta({\bf r} - {\bf r}_i).
\end{displaymath}">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$I$">|; 

$key = q/displaystyle0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="$\displaystyle 0,$">|; 

$key = q/{displaymath}dP=langle{{bf{u}(r,theta,varphi)rangle!cdot!{hat{{bf{r}},,r^2,d{mitOmega}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2267.png"
 ALT="\begin{displaymath}
dP = \langle {\bf u}(r, \theta, \varphi)\rangle\!\cdot\!{\hat{\bf r}}  r^2 d{\mit\Omega}.
\end{displaymath}">|; 

$key = q/{displaymath}partial^muA_mu=partial_muA^mu=nabla!cdot!{{bf{A}+frac{1}{c}frac{partialA^0}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img2912.png"
 ALT="\begin{displaymath}
\partial^\mu A_\mu = \partial_\mu A^\mu =
\nabla\!\cdot \! {\bf A} + \frac{1}{c}\frac{\partial A^0}
{\partial t}.
\end{displaymath}">|; 

$key = q/{displaymath}intint_Sx^2,y,dx,dy{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="\begin{displaymath}
\int\int_S x^2  y dx dy
\end{displaymath}">|; 

$key = q/{displaymath}E_r(r>a)=frac{Q}{4pi,epsilon_0,r^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="\begin{displaymath}
E_r(r&gt;a) = \frac{Q}{4\pi  \epsilon_0  r^2}.
\end{displaymath}">|; 

$key = q/d{{bf{l}=(dx,,dy,,dz);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$d{\bf l}= (dx, dy, dz)$">|; 

$key = q/{displaymath}phi({{bf{r})rightarrowphi({{bf{r})+c{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="\begin{displaymath}
\phi({\bf r}) \rightarrow \phi({\bf r}) + c
\end{displaymath}">|; 

$key = q/dy=y-y_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$dy=y-y_0$">|; 

$key = q/displaystyledelta_a^j,delta_b^k-delta_b^j,delta_a^k,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3007.png"
 ALT="$\displaystyle \delta_a^j  \delta_b^k - \delta_b^j \delta_a^k,$">|; 

$key = q/{displaymath}mu=mu_0,(1+chi_m){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1795.png"
 ALT="\begin{displaymath}
\mu = \mu_0 (1+ \chi_m)
\end{displaymath}">|; 

$key = q/displaystyle-mu_0,{{bf{j}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="$\displaystyle - \mu_0  {\bf j}.$">|; 

$key = q/displaystyle-frac{partial{{bf{B}}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="$\displaystyle - \frac{\partial {\bf B}}{\partial t} ,$">|; 

$key = q/{displaymath}{mitdiv},{{bf{A}=lim_{dVrightarrow0}frac{oint{{bf{A}cdotd{{bf{S}}{dV}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="\begin{displaymath}
{\mit div} {\bf A} = \lim_{dV\rightarrow 0} \frac{\oint {\bf A}\cdot d{\bf S}}
{dV}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{curl,A}=nablatimes{{bf{A}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="\begin{displaymath}
{\bf curl  A} = \nabla\times{\bf A}
\end{displaymath}">|; 

$key = q/(c,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1524.png"
 ALT="$(c, 0, 0)$">|; 

$key = q/{displaymath}I=frac{langle{{bf{E}times{{bf{B}cdothat{{bf{z}rangle}{mu_0}=frac{E_0,B_0}{2,mu_0}=frac{E_0^{,2}}{2,mu_0,v}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img2482.png"
 ALT="\begin{displaymath}
I =\frac{\langle {\bf E}\times{\bf B}\cdot\hat{\bf z}\rangle...
...0}= \frac{E_0 B_0}{2 \mu_0} = \frac{E_0^{ 2}}{2 \mu_0 v}.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{f}=q,{{bf{v}times{{bf{B}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="\begin{displaymath}
{\bf f} = q {\bf v} \times{\bf B}.
\end{displaymath}">|; 

$key = q/R_{{rm{load};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2245.png"
 ALT="$R_{\rm load}$">|; 

$key = q/{displaymath}k^2=mu_0,omega,(epsilon,epsilon_0,omega+{{rm{i},sigma).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2399.png"
 ALT="\begin{displaymath}
k^2 = \mu_0 \omega (\epsilon \epsilon_0 \omega + {\rm i} \sigma).
\end{displaymath}">|; 

$key = q/{displaymath}F(z)=z-frac{c^2}{z},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1579.png"
 ALT="\begin{displaymath}
F(z) = z - \frac{c^2}{z},
\end{displaymath}">|; 

$key = q/displaystylealpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1740.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/displaystyle{{bf{something},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$\displaystyle {\bf something},$">|; 

$key = q/E^{23};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3070.png"
 ALT="$E^{23}$">|; 

$key = q/displaystylec,A_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3113.png"
 ALT="$\displaystyle c A_3$">|; 

$key = q/F(z)=z^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1591.png"
 ALT="$F(z) = z^{1/2}$">|; 

$key = q/displaystyleE_t=left(frac{2}{1+alpha,beta}right)E_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2542.png"
 ALT="$\displaystyle E_t = \left(\frac{2}{1+\alpha \beta}\right) E_i.$">|; 

$key = q/displaystyleT^{2'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2882.png"
 ALT="$\displaystyle T^{2'}$">|; 

$key = q/{{bf{b},equiv,stackrel{displaystylerightarrow}{QR},equiv,stackrel{displaystylerightarrow}{PS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="${\bf b}  \equiv  \stackrel{\displaystyle \rightarrow}{QR} \equiv
 \stackrel{\displaystyle \rightarrow}{PS}$">|; 

$key = q/displaystylefrac{d^2Y}{dy^2}=-k^2,Y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1615.png"
 ALT="$\displaystyle \frac{d^2 Y}{d y^2} = - k^2 Y.$">|; 

$key = q/displaystyleV(x,y);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1545.png"
 ALT="$\displaystyle V(x, y)$">|; 

$key = q/{displaymath}int_{S_1}{{bf{A}cdotd{{bf{S}=int_{S_2}{{bf{A}cdotd{{bf{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="\begin{displaymath}
\int_{S_1} {\bf A}\cdot d{\bf S} = \int_{S_2} {\bf A}\cdot d{\bf S}.
\end{displaymath}">|; 

$key = q/0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="$0.1$">|; 

$key = q/langlecos(omega,t),sin(omega,t)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2021.png"
 ALT="$\langle \cos(\omega  t) \sin(\omega  t)\rangle = 0$">|; 

$key = q/displaystylephi_S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1406.png"
 ALT="$\displaystyle \phi_S$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1881.png"
 ALT="$M$">|; 

$key = q/{displaymath}f_nu=-partial_mu{T^mu}_nu,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img3195.png"
 ALT="\begin{displaymath}
f_\nu = - \partial_\mu {T^\mu}_\nu,
\end{displaymath}">|; 

$key = q/{{bf{U}={{bf{A}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1463.png"
 ALT="${\bf U}={\bf A}_3$">|; 

$key = q/{displaymath}{{bf{E}=frac{1}{4pi,epsilon_0}intleft([rho],frac{{bf{R}{R^3}+left[f{[partial{{bf{j}slashpartialt]}{c^2R}right),dV',{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="\begin{displaymath}
{\bf E} = \frac{1}{4\pi \epsilon_0} \int \left(
[\rho]  \f...
...2}
- \frac{[\partial {\bf j}/\partial t]}{c^2 R} \right) dV',
\end{displaymath}">|; 

$key = q/u({{bf{r},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="$u({\bf r}, t)$">|; 

$key = q/displaystyle{{rm{i},omega,B_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2579.png"
 ALT="$\displaystyle {\rm i} \omega B_y$">|; 

$key = q/{displaymath}nablatimes{{bf{B}=mu_0,I,delta(x),delta(y),hat{{bf{z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="\begin{displaymath}
\nabla\times{\bf B} = \mu_0  I \delta(x) \delta(y) \hat{\bf z}.
\end{displaymath}">|; 

$key = q/displaystyle-mu_0,j_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$\displaystyle - \mu_0  j_y,$">|; 

$key = q/E_perp=Vslashd;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="$E_\perp = V/d$">|; 

$key = q/displaystylefrac{dv_y}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$\displaystyle \frac{dv_y}{dt}$">|; 

$key = q/|{{bf{r}-{{bf{r}'|rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="$\vert{\bf r} - {\bf r}'\vert\rightarrow 0$">|; 

$key = q/nablacdot{{bf{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$\nabla\cdot {\bf B} $">|; 

$key = q/{displaymath}B^{ij}=B_{ij}=left(array{{ccc}0&B_z&-B_y[0.5ex]-B_z&0&B_x[0.5ex]B_y&-B_x&0array{right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="84" BORDER="0"
 SRC="|."$dir".q|img3019.png"
 ALT="\begin{displaymath}
B^{ij}=B_{ij} = \left(\begin{array}{ccc}
0&amp; B_z &amp; -B_y [0....
...
-B_z &amp; 0 &amp; B_x  [0.5ex]
B_y &amp; -B_x &amp; 0 \end{array} \right),
\end{displaymath}">|; 

$key = q/displaystyleE_i,(costheta_i,,0,,-sintheta_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2546.png"
 ALT="$\displaystyle E_i (\cos\theta_i,  0, -\sin\theta_i),$">|; 

$key = q/displaystyleT^{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3206.png"
 ALT="$\displaystyle T^{ij}$">|; 

$key = q/{displaymath}{{bf{D}=epsilon_0,mbox{{boldmath{{epsilon{}!cdot!{{bf{E},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1687.png"
 ALT="\begin{displaymath}
{\bf D} = \epsilon_0  \mbox{\boldmath$ \epsilon$}\!\cdot\!{\bf E},
\end{displaymath}">|; 

$key = q/r=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="$r=0$">|; 

$key = q/u_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="$u_1$">|; 

$key = q/ds^2=g_{ij},dx^i,dx^j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2862.png"
 ALT="$ds^2 = g_{ij} dx^i  dx^j$">|; 

$key = q/displaystylembox{hspace{4cm}}-frac{partial}{partialx}!left(frac{1}{[(x-x')^2+(y-y')^2+(z-z')^2]^{~1slash2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="563" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="$\displaystyle \mbox{\hspace{4cm}}-\frac{\partial}{\partial x}\!\left(
\frac{1}{[(x-x')^2+(y-y')^2 + (z-z')^2]^{&nbsp;1/2}}\right).$">|; 

$key = q/displaystylefrac{v_perp}{mitOmega},sin({mitOmega},t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$\displaystyle \frac{v_\perp}{\mit\Omega} \sin({\mit\Omega} t),$">|; 

$key = q/nablacdot{{bf{A}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="$\nabla\cdot {\bf A} = 0$">|; 

$key = q/l,x+m,y+n,z+p=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2691.png"
 ALT="$l x + m  y + n  z + p=0$">|; 

$key = q/{displaymath}frac{partialV}{partialx}=-L,frac{partialI}{partialt}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2048.png"
 ALT="\begin{displaymath}
\frac{\partial V}{\partial x} = - L \frac{\partial I}{\partial t}.
\end{displaymath}">|; 

$key = q/sigmaggepsilon,epsilon_0,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2406.png"
 ALT="$\sigma\gg \epsilon \epsilon_0 \omega$">|; 

$key = q/{{bf{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="${\bf v}$">|; 

$key = q/r'=-c,t';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3118.png"
 ALT="$r'= -c t'$">|; 

$key = q/partialslashpartialx^i|_{t'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3242.png"
 ALT="$\partial/
\partial x^i\vert _{t'}$">|; 

$key = q/(x',y',z',t');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2698.png"
 ALT="$(x', y', z', t')$">|; 

$key = q/{displaymath}frac{d{{bf{a}}{dt}=mbox{{boldmath{{omega{}times{{bf{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="\begin{displaymath}
\frac{d {\bf a}}{dt} = \mbox{\boldmath$\omega$}\times {\bf a}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{rho}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$\displaystyle - \frac{\rho}{\epsilon_0},$">|; 

$key = q/45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$45^\circ$">|; 

$key = q/{displaymath}gamma=(1-v^2slashc^2)^{-1slash2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2746.png"
 ALT="\begin{displaymath}
\gamma = (1-v^2/c^2)^{-1/2}
\end{displaymath}">|; 

$key = q/{displaymath}frac{partials}{partialt'}=frac{partialr}{partialt'}-frac{{{bf{r}!cd}-frac{{{bf{r}!cdot!dot{{bf{u}}{c}+frac{u^2}{c}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img3254.png"
 ALT="\begin{displaymath}
\frac{\partial s}{\partial t'} = \frac{\partial r}{\partial ...
...}{r} - \frac{
{\bf r}\!\cdot\!\dot{\bf u}}{c} + \frac{u^2}{c}.
\end{displaymath}">|; 

$key = q/z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$z'$">|; 

$key = q/mllM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2139.png"
 ALT="$m\ll M$">|; 

$key = q/{displaymath}frac{4pi,epsilon_0}{e},{{bf{E}=frac{nabla's}{s^2}-frac{{{bf{r}}{s^3ac{r,{{bf{u}}{s^3,c^2}frac{partials}{partialt'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img3252.png"
 ALT="\begin{displaymath}
\frac{4\pi  \epsilon_0}{e}  {\bf E} = \frac{\nabla' s}{s^2...
...+ \frac{r {\bf u}}{s^3  c^2} \frac{\partial s}{\partial t'}.
\end{displaymath}">|; 

$key = q/r^2=x^2+y^2+z^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$r^2=x^2+y^2+z^2$">|; 

$key = q/{displaymath}{{bf{j}=-e,n_e,{{bf{v}=frac{{{rm{i},n_e,e^2,{{bf{E}}{m_e,(omega+{{rm{i},nu)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img2429.png"
 ALT="\begin{displaymath}
{\bf j} = - e n_e {\bf v} = \frac{{\rm i} n_e e^2  {\bf E}}{m_e (\omega+{\rm i} \nu)},
\end{displaymath}">|; 

$key = q/{displaymath}g^{ij}g_{jk}=delta_k^i.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img2835.png"
 ALT="\begin{displaymath}
g^{ij} g_{jk} = \delta_k^i.
\end{displaymath}">|; 

$key = q/qslashepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$q/\epsilon_0$">|; 

$key = q/Q^mu=({{bf{q},k);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2901.png"
 ALT="$Q^\mu = ({\bf q}, k)$">|; 

$key = q/{displaymath}nablacdot(phi,{{bf{A})=phi,nablacdot{{bf{A}+{{bf{A}cdotnablaphi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="239" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="\begin{displaymath}
\nabla\cdot (\phi {\bf A}) =\phi  \nabla\cdot {\bf A} + {\bf A}\cdot \nabla\phi
\end{displaymath}">|; 

$key = q/{displaymath}m_e,frac{d{{bf{v}}{dt}=-e,({{bf{E}+B_0,{{bf{v}timeshat{{bf{z}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2353.png"
 ALT="\begin{displaymath}
m_e \frac{d{\bf v}}{dt} = -e ({\bf E} + B_0 {\bf v}\times\hat{\bf z}),
\end{displaymath}">|; 

$key = q/ds^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2833.png"
 ALT="$ds^2$">|; 

$key = q/{figure}{epsfysize{=2in{centerline{epsffile{fig3.eps}}{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="\begin{figure}
\epsfysize =2in
\centerline{\epsffile{fig3.eps}}
\end{figure}">|; 

$key = q/{displaymath}frac{|{{bf{f}_{{rm{electrical}|}{|{{bf{f}_{{rm{gravitational}|}=4.17times10^{42}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="\begin{displaymath}
\frac{\vert{\bf f}_{\rm electrical}\vert}{\vert{\bf f}_{\rm gravitational}\vert}
= 4.17\times 10^{42}.
\end{displaymath}">|; 

$key = q/E_{{rm{crit}sim10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="$E_{\rm crit} \sim 10^6$">|; 

$key = q/m_e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2270.png"
 ALT="$m_e$">|; 

$key = q/{displaymath}theta_0=cos^{-1}(uslashc).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img3376.png"
 ALT="\begin{displaymath}
\theta_0 = \cos^{-1}(u/c).
\end{displaymath}">|; 

$key = q/x^2+y^2+z^2rightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1488.png"
 ALT="$x^2+y^2+z^2\rightarrow\infty$">|; 

$key = q/{displaymath}l,Bsimepsilon_0mu_0,frac{E,l^2}{t},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="\begin{displaymath}
l  B \sim \epsilon_0 \mu_0  \frac{ E  l^2}{t},
\end{displaymath}">|; 

$key = q/hat{{bf{k}=+hat{{bf{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2447.png"
 ALT="$\hat{\bf k} = +\hat{\bf z}$">|; 

$key = q/{displaymath}phi(Q)-phi(P)=int_P^Qnablaphicdotd{{bf{l}=-int_P^Q{{bf{E}cdotd{{bf{l}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="\begin{displaymath}
\phi(Q) - \phi(P) = \int_P^Q \nabla\phi \cdot d{\bf l} = -
\int_P^Q {\bf E} \cdot d{\bf l}.
\end{displaymath}">|; 

$key = q/{displaymath}nablatimesleft({{bf{E}+frac{partial{{bf{A}}{partialt}right)={{bf{0}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="\begin{displaymath}
\nabla\times\left( {\bf E} + \frac{\partial {\bf A} }{\partial t} \right) ={\bf0}.
\end{displaymath}">|; 

$key = q/nablacdot{{bf{E}={{bf{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1729.png"
 ALT="$\nabla\cdot{\bf E}={\bf0}$">|; 

$key = q/{displaymath}{mitdiv}left(kappa,{{bf{grad},Tright)=c,frac{partialT}{partialt},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="\begin{displaymath}
{\mit div}\left(\kappa  {\bf grad}  T\right) = c \frac{\partial T}{\partial t},
\end{displaymath}">|; 

$key = q/R=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="$R = 1$">|; 

$key = q/{displaymath}W=-int_P^Q{{bf{f}cdotd{{bf{l}=-qint_P^Q{{bf{E}cdotd{{bf{l}=qint_P^Qnablaphicdotd{{bf{l}=qleft[phi(Q)-phi(P)right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="540" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="\begin{displaymath}
W =- \int_P^Q {\bf f} \cdot d{\bf l} =- q \int_P^Q {\bf E} \...
...\nabla\phi \cdot d{\bf l} = q \left[ \phi(Q) - \phi(P)\right].
\end{displaymath}">|; 

$key = q/N_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1907.png"
 ALT="$N_1$">|; 

$key = q/{displaymath}{{bf{E}({{bf{r})=frac{1}{4pi,epsilon_0}intrho({{bf{r}'),frac{{{bf{r}-{{bf{r}'}{|{{bf{r}-{{bf{r}'|^3},d^3{{bf{r}'.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="\begin{displaymath}
{\bf E}({\bf r}) = \frac{1}{4\pi  \epsilon_0} \int \rho({\b...
...f r} - {\bf r}'}{\vert{\bf r} - {\bf r}'\vert^3} d^3{\bf r}'.
\end{displaymath}">|; 

$key = q/{displaymath}|{{bf{a}times{{bf{b}|=|a|,|b|,sintheta.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="\begin{displaymath}
\vert{\bf a}\times{\bf b}\vert = \vert a\vert \vert b\vert \sin\theta.
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{E}=E_0left[cos(k,z-omega,t),cos({mitDelta}k,z),,cos(k,z-omega,t),sin({mitDelta}k,z),,0right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="497" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img2385.png"
 ALT="\begin{displaymath}
{\bf E} =E_0 \left[\cos(k z-\omega t) \cos({\mit\Delta} k...
..., 
\cos(k z-\omega t) \sin({\mit\Delta} k z),  0\right].
\end{displaymath}">|; 

$key = q/displaystylenablatimes{{bf{B}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1453.png"
 ALT="$\displaystyle \nabla\times{\bf B}_1$">|; 

$key = q/dy';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2662.png"
 ALT="$dy'$">|; 

$key = q/-nabla!cdot!{{bf{P};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1671.png"
 ALT="$-\nabla\!\cdot\!{\bf P}$">|; 

$key = q/(0,1slashsqrt{2},1slashsqrt{2},1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2678.png"
 ALT="$(0, 1/\sqrt{2}, 1/\sqrt{2},
1)$">|; 

$key = q/{{bf{A}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1467.png"
 ALT="${\bf A}_3$">|; 

$key = q/displaystylefrac{u'_3}{gamma,(1+u'_1,vslashc^2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2752.png"
 ALT="$\displaystyle \frac{u'_3}{\gamma (1+u'_1  v/c^2)}.$">|; 

$key = q/2pi,a^3slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$2\pi  a^3/3$">|; 

$key = q/{displaymath}{{bf{u}={{bf{E}times{{bf{H},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img2134.png"
 ALT="\begin{displaymath}
{\bf u} = {\bf E}\times{\bf H},
\end{displaymath}">|; 

$key = q/{displaymath}V_0=I_0left({{rm{i},omega,L+frac{1}{{{rm{i},omega,C}+Rright).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img2012.png"
 ALT="\begin{displaymath}
V_0 = I_0 \left({\rm i} \omega  L + \frac{1}{{\rm i} \omega  C} + R\right).
\end{displaymath}">|; 

$key = q/displaystyleleft(frac{2,n_1}{n_1+n_2}right)E_t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2475.png"
 ALT="$\displaystyle \left(\frac{2  n_1}{n_1+n_2}\right) E_t.$">|; 

$key = q/{displaymath}m=gamma,m_0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img3158.png"
 ALT="\begin{displaymath}
m = \gamma  m_0.
\end{displaymath}">|; 

$key = q/{{bf{B}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2502.png"
 ALT="${\bf B}_i$">|; 

$key = q/gammagg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3146.png"
 ALT="$\gamma\gg 1$">|; 

$key = q/dE=dW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="$dE = dW$">|; 

$key = q/{displaymath}V=oint_C{{bf{E}cdotd{{bf{l}=A,frac{partial}{partialt}!int_S{{bf{B}cdotd{{bf{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="\begin{displaymath}
V = \oint_C{\bf E} \cdot d{\bf l} = A  \frac{\partial }{\partial t}\!
\int_S {\bf B} \cdot d{\bf S},
\end{displaymath}">|; 

$key = q/{displaymath}alpha=E_0,a^3.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img1653.png"
 ALT="\begin{displaymath}
\alpha = E_0 a^3.
\end{displaymath}">|; 

$key = q/V_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1473.png"
 ALT="$V_0$">|; 

$key = q/{displaymath}I=frac{4}{9}frac{epsilon_0,A}{d^2}left(frac{2,e}{m_e}right)^{1slash2}V_0^{3slash2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1484.png"
 ALT="\begin{displaymath}
I = \frac{4}{9}\frac{\epsilon_0 A}{d^2}\left(\frac{2 e}{m_e}\right)^{1/2}
V_0^{3/2}.
\end{displaymath}">|; 

$key = q/{displaymath}sintheta_i=frac{k_{x,i}}{k_i},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img2512.png"
 ALT="\begin{displaymath}
\sin\theta_i = \frac{k_{x i}}{k_i},
\end{displaymath}">|; 

$key = q/displaystyleE_t,hat{{bf{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2531.png"
 ALT="$\displaystyle E_t \hat{\bf y},$">|; 

$key = q/displaystylep_{mu'}^{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2891.png"
 ALT="$\displaystyle p_{\mu'}^{\mu}$">|; 

$key = q/{displaymath}frac{partial^2V}{partialx^2}=-frac{partial}{partialx}frac{partialU}frac{partial}{partialy}frac{partialV}{partialy},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1562.png"
 ALT="\begin{displaymath}
\frac{\partial^2 V}{\partial x^2} = -\frac{\partial}{\partia...
... - \frac{\partial}{\partial y} \frac{\partial V}
{\partial y},
\end{displaymath}">|; 

$key = q/k>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1622.png"
 ALT="$k&gt;0$">|; 

$key = q/10^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="$10^5$">|; 

$key = q/{displaymath}phi(x,y)=sum_{n=1}^inftyC_nexp(-n,x)sin(n,y),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1628.png"
 ALT="\begin{displaymath}
\phi(x, y) = \sum_{n=1}^\infty C_n \exp(-n  x) \sin (n y),
\end{displaymath}">|; 

$key = q/n_1=1.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2564.png"
 ALT="$n_1=1.0$">|; 

$key = q/{{bf{E}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1845.png"
 ALT="${\bf E}'$">|; 

$key = q/{displaymath}phi({{bf{r},t)=frac{rho({{bf{r}',t')}{4pi,epsilon_0}frac{delta(t-t'-|{{bf{r}-{{bf{r}'|slashc)}{|{{bf{r}-{{bf{r}'|},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="\begin{displaymath}
\phi({\bf r}, t) = \frac{\rho({\bf r}' ,t ')} {4\pi  \epsil...
...vert{\bf r} - {\bf r}'\vert/c)}{\vert{\bf r} - {\bf r}'\vert},
\end{displaymath}">|; 

$key = q/{displaymath}{{bf{A}={{bf{grad},V.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="\begin{displaymath}
{\bf A} = {\bf grad}  V.
\end{displaymath}">|; 

$key = q/displaystyleBox^2{{bf{E};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="$\displaystyle \Box^2 {\bf E}$">|; 

$key = q/ds^2=(dx^1)^2+(dx^2)^2+cdots+(dx^n)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2832.png"
 ALT="$ds^2 = (dx^1)^2 +(dx^2)^2 + \cdots + (dx^n)^2$">|; 

$key = q/k=-VslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1900.png"
 ALT="$k=-V/R$">|; 

$key = q/{displaymath}P_{{rm{load}=frac{E_0^{,2},l^2}{8,R_{{rm{rad}}=frac{epsilon_0,c,E_0^{,2}}{2},A_{{rm{eff},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img2259.png"
 ALT="\begin{displaymath}
P_{\rm load} =\frac{ E_0^{ 2}  l^2}{8  R_{\rm rad} } = \frac{\epsilon_0  c  E_0^{ 2}}{2}
 A_{\rm eff},
\end{displaymath}">|; 

$key = q/B_c=mu,H_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1838.png"
 ALT="$B_c = \mu H_c$">|; 

$key = q/oint{{bf{A}cdotd{{bf{l};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$\oint {\bf A}\cdot d{\bf l}$">|; 

$key = q/a_j,a_jequiv{{bf{a}cdot{{bf{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2169.png"
 ALT="$a_j a_j\equiv {\bf a}\cdot{\bf a}$">|; 

$key = q/nabla!cdot!{{bf{E}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1712.png"
 ALT="$\nabla\!\cdot\!{\bf E} = 0$">|; 

$key = q/{{bf{b}=(0,,1,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="${\bf b} = (0, 1, 0)$">|; 

$key = q/{displaymath}E_y={{rm{i}left(-omega,frac{partialB_z}{partialx}+k,frac{partialE_zly}right)left(frac{omega^2}{c^2}-k^2right)^{-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img2591.png"
 ALT="\begin{displaymath}
E_y = {\rm i}\left(-\omega \frac{\partial B_z}{\partial x} ...
...{\partial y}\right)\left(\frac{\omega^2}{c^2}-k^2\right)^{-1},
\end{displaymath}">|; 

$key = q/10^1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$10^1$">|; 

$key = q/{{bf{a}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="${\bf a}'$">|; 

1;

